Practice Question 2

Question

Two cars are traveling north along a highway. The first drives at 40 mph, and the second, which leaves 3 hours later, travels at 60 mph. How long after the second car leaves will it take for the second car to catch the first?

A. 6 hours 40 minutes

B. 2 hours

C. 6 hours

D. 5 hours

E. 1 hour 12 minutes

Answer 1

Let the time taken by the first car =T

Distance =Time x speed

 

40T = 60*(T - 3)

40T =60T - 180

60T - 40T = 180

T = 9 hours for the first car, or:

9 - 3 = 6 hours for the second car - when it catches up with the first car.



Check: 40 mph x 9 hours =60 mph x 6 hours =360 miles covered.

Answer 2

In 3 hours, car 1 goes 120 miles. Car 2 has to catch up 120 miles.

4 hours (1 hour after 2nd car starts): 1 160; 2 60 = 100 miles to catch up.

5 hours: 1 200, 2 120 = 80 miles to catch up. Notice, car 2 is catching up 20 miles every hour.

Car 2 started 120 miles behind. 120/20 = 6 hours

C