Bus A is 150 miles due east of Bus B Both busses start drivi

Bus A is 150 miles due east of Bus B. Both busses start driving due west at constant speeds at the same time. It takes Bus A 10 hours to overtake Bus B. If they had started out at the same time, had driven at the same constant speeds, but had driven toward one another, they would have met in 2 hours. What is the speed, in miles per hour, of Bus A?

Solution

Let the speed of bus A = x mph
And,the speed of bus B = y mph
Bus A is 150 miles due east of Bus B
Both busses start driving due west at constant speeds at the same time. It takes Bus A 10 hours to overtake Bus B.
So, 10(x-y) = 150 [ time*speed = distance]
x-y = 15 ...(1)
Also,if had driven toward one another, they would have met in 2 hours.
2(x+y) = 150
x+y = 75 ...(2)
(1)+(2)=> 2x = 90
x = 45
(2)=> 45+y = 75
y = 75-45
y = 30
Therefore, the speed of bus A = 45 mph
And,the speed of bus B = 30 mph