Answer:
63 miles per hour
54 miles per hour
Explanation:
Let the two buses be represented as bus A and bus B.
bus A and bus B leave a station at the same time and travel in opposite directions.
Let the speed of bus A be A miles per hour.
Let the speed of bus B be B miles per hour.
One bus travels 9 miles/hour slower than the other.
Let bus A be the faster bus.
This means that the speed of bus B is B = A - 9
If the two buses are 585 miles apart after 5hours, this means that after 5hours, the total distance travelled by bus A and bus B is 585 miles.
Distance travelled by bus A in 5 hours = speed × time = 5A
Distance travelled by bus B in 5 hours = speed × time = 5B
5A + 5B = 585 - - - - - -1
Substituting B = A - 9 in equation 1
5A + 5(A - 9) = 585
5A + 5A - 45 = 585
10A = 585 + 45 = 630
A = 630/10 = 63 miles per hour
B = A - 9 = 63 - 9 = 54 miles per hour