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The equation d=rt represents the formula for total distance traveled. The distance traveled, d, is equal to the rate of travel, r, multiplied by the time of travel, t. Use this formula to help solve the following problem.
Tina and Tim work together and are planning to take a trip this weekend. On Friday afternoon, Tina gets a head start and leaves work in her car traveling at 45 mph. Three hours later, Tim leaves work on the same road at 65 mph. Assuming there is no traffic, in how many hours will Tim pass Tina?
A. Who will be driving longer and by how much?
B. Once Tim catches up with Tina, who will have gone the farther distance?
C. What equation represents this situation?
D. Solve the equation; show your work
E. How many hours did it take Tim to pass Tina?
I'll solve the problem and let you answer the above questions from that:
Let t = time for Tim to catch up with Tina
(t+3) = Tina's travel time, when Tim catches up
When Tim catches Tina they will have gone the same distance (ans question B)
Write a distance equation from this fact; Dist = speed * time:
Tim's dist = Tina's dist
65t = 45(t+3)
65t = 45t + 135
65t - 45t = 135
20t = 135
t = 6.75 hrs for Tim to catch up with Tina
Confirm our solution by finding the distance traveled by each (should be equal):
(Tina' travel time: 6.75 + 3 = 9.75)
9.75 * 45 = 438.75 mi
6.75 * 65 = 438.75 mi