Algebra 1 Ch 2.4 – Solving Equations with Variables on Both Sides.
VARIABLES ON BOTH SIDES STORY PROBLEMS
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Transcript of VARIABLES ON BOTH SIDES STORY PROBLEMS
VARIABLES ON BOTH SIDES
STORY PROBLEMS
“THE TOUGH STUFF”
A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?
Cost for Rent-a-wreck = 60 + .2m
A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?
Cost for Rent-a-wreck = 60 + .2m Cost for Lemon Leasers = 30 + .5m
A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?
Cost for Rent-a-wreck = 60 + .2m Cost for Lemon Leasers = 30 + .5m Set the two equal to each other
A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?
Cost for Rent-a-wreck = 60 + .2m Cost for Lemon Leasers = 30 + .5m Set the two equal to each other 60 + .2m = 30 + .5m
A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
This is a “same direction” problem.
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
This is a “same direction” problem. When going the same direction, the
distances are equal.
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
This is a “same direction” problem. When going the same direction, the
distances are equal. Use the formula d = rt
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time Distance
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time DistanceJoe
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time DistanceJoeJane
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time DistanceJoe 6Jane
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time DistanceJoe 6Jane 8
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time DistanceJoe 6 tJane 8
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time DistanceJoe 6 tJane 8 t - 15
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time DistanceJoe 6 t 6tJane 8 t - 15
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time DistanceJoe 6 t 6tJane 8 t - 15 8(t – 15)
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Set the distances equal to each other and solve.
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Set the distances equal to each other and solve.
6 𝑡=8(𝑡−15)
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Set the distances equal to each other and solve.
6 𝑡=8(𝑡−15)6 𝑡=8𝑡−120
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Set the distances equal to each other and solve.
6 𝑡=8(𝑡−15)6 𝑡=8𝑡−120−2 𝑡=−120
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Set the distances equal to each other and solve.
6 𝑡=8(𝑡−15)6 𝑡=8𝑡−120−2 𝑡=−120𝑡=60
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time DistanceJoe 6 t 6tJane 8 t - 15 8(t – 15)
The t solved for was the time that JOE was on the road.
Jane’s time was (t – 15), or 45 minutes.
Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?
Rate Time DistanceJoe 6 t 6tJane 8 t - 15 8(t – 15)
**BE SURE TO ANSWER THE QUESTION ASKED.
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
WillWayne
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50Wayne
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50Wayne 70
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 tWayne 70
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 tWayne 70 t - 2
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 6:00 amWayne 70 t - 2
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 6:00 amWayne 70 t - 2 8:00 am
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 8:00 am
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am
50 𝑡=70(𝑡−2)
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am
50 𝑡=70(𝑡−2)50 𝑡=70 𝑡−140
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am
50 𝑡=70(𝑡−2)50 𝑡=70 𝑡−140−20 𝑡=−140
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am
50 𝑡=70(𝑡−2)50 𝑡=70 𝑡−140−20 𝑡=−140𝑡=7h𝑟𝑠
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am
Is 7 hours the answer to the question??
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am
Is 7 hours the answer to the question??
This question asked for “what time”. That means the actual clock time.
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am
Since t was the time for Will, add 7 hours to his departure time.
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am
Since t was the time for Will, add 7 hours to his departure time.Will left at 6:00 am. Wayne catches him 7 hours later, or at 1:00 pm
Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?
Rate Time Distance
Clock
Will 50 t 50t 6:00 amWayne 70 t - 2 70(t – 2) 8:00 am
Since t was the time for Will, add 7 hours to his departure time.Will left at 6:00 am. Wayne catches him 7 hours later, or at 1:00 pm**Be sure to include the proper am vs. pm designation
7-5: 17, 28, 33, 35 - 40
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