Question

A car leaves a city with a speed of 90 mph. Three hours later and out of the same city another car in pursuit of the first leaves with a speed of 120 mph. Find the time it takes for the second car to reach the first.

Answer 1

9 hours

Step-by-step explanation:

When the 2nd car catches up to the first, both cars will have gone the same distance.

Distance = rate x time

Distance car 1 traveled when car 2 catches up = 90 mph(3 hr + t)

Distance car 2 traveled when it catches up to car 1 = 120t

90(3 + t) = 120t

270 + 90t = 120t

30t = 270

t = 270/30 = 9 hrs

Therefore, 12 hours after car 1 leaves the city and 9 hours after car 2 leaves the same city, they meet up.

To prove it:

90(12) = 120(9) = 1080 Car 2 catches up to Car 1 1080 miles from the city