A bus left the city traveling an avg. of 60 m/h. An hour later a car left at 75 m/h. How long will it take the car to catch the bus?

Expert Answers
lemjay eNotes educator| Certified Educator

Let's apply the formula of average speed which is 

`s= d/t`

where s - average speed , d - distance travelled and t - time of travel.

For the bus, let `s_1` be its average speed and t its time of travel.Then, express its distance travelled in terms of t. So,

`d_1 = s_1 t`

Substituting value of `s_1` yields:


And for the car , let `s_2` be its average speed. Since the car left one hour after the bus left, its time of travel is one less than t (time of bus).In math form, it is express as t-1. So the equation of the distance travelled by the car in terms of t is:



To simplify, distribute 75 to t-1.


To solve for he time of travel of the car, when it caught up with the bus, set the two distances equal to each other.



Then. combine like terms. To do so, subtract both sides by 75t.

`60t-75t=75t-75t - 75`



And, divide both  sides by -15 to isolate t.



This means that the bus has already travelled for 5 hours when the car caught up with it.

Since the car left one hour after, then its time of travel is:

`t - 1 = 5-1 = 4`

Hence, it took the car 4 hours to catch up with the bus.