Question

Two buses leave a station at the same time and travel in opposite directions. One bus travels 9 mi h slower than the other. If the two buses are 585 miles apart after 5 hours, what is the rate of each bus?

Answer 1

Answer: rate of bus A = 63 miles per hour

rate of bus B = 54 miles per hour

Step-by-step explanation:

Let the buses be bus A and bus B

Let a = the speed of bus A.

Let b = the speed of bus B

One bus travels 9 miles/hr slower than the other. Assuming Bus A is the faster bus, it means

x = y + 9 - - - - - - - -1

If the two buses are 585 miles apart after 5 hours, it means that both of them have travelled a total of 585 miles after they left the station.

Speed = distance / time

Distance = speed × time

In 5 hours, Bus A would have travelled a distance of x × 5 = 5x miles.

Also, In 5 hours, Bus B would have travelled a distance of y × 5 = 5y miles.

Since total distance travelled is 585 miles, therefore,

5x + 5y = 585 - - - - - - - - -2

Substituting x = y + 9 into equation 2, it becomes

5(y + 9) + 5y = 585

5y + 45 + 5y = 585

5y + 5y = 585 - 45

10y = 540

y = 540/10 = 54 miles per hour

x = y + 9 = 54 + 9

x = 63 miles per hour