Answer: rate of bus A = 63 miles per hour
rate of bus B = 54 miles per hour
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