SOLUTION: Students are traveling in two cars to a football game 135 miles away. The first car travels at an average speed of 45 miles per hour. The second car starts one-half hour after the

Question 112918: Students are traveling in two cars to a football game 135 miles away. The first car travels at an average speed of 45 miles per hour. The second car starts one-half hour after the first and travels at an average speed of 55 miles per hour. How long will it take the second car to catch up to the first car? Will the second car catch up to the first car before the first car arrives at the game?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
: Students are traveling in two cars to a football game 135 miles away. The first car travels at an average speed of 45 miles per hour. The second car starts one-half hour after the first and travels at an average speed of 55 miles per hour. How long will it take the second car to catch up to the first car? Will the second car catch up to the first car before the first car arrives at the game?
:
Let t = travel time of the 2nd car to catch up with the 1st car
then
(t+.5) = travel time of the 1st car when it is caught
:
We know when one car catches up with the other they will have traveled the same dist:
Write a dist equation: Dist = speed * time
:
2nd car dist = 1st car dist
55t = 45(t+.5)
55t = 45t + 22.5
55t - 45t = 22.5
10t = 22.5
t = 22.5/10
t = 2.25 hrs travel time of the 2nd car
then
2.25 + .5 = 2.75 hrs travel time of the 1st car
:
Find the distance, if it is less than 135 mi he will catch up with 1st car
45 * 2.75 = 123.75 mi
55 * 2.25 = 123.75 mi also
:
We can say he will catch up; 135 - 123.75 = 11.25 mi before their destination
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