Answer: speed of the first bus is 81 miles per hour.
speed of the second bus is 69 miles per hour.
Step-by-step explanation:
Let x = the speed of the first bus
Let y = speed of the second bus
One bus travels 12 miles/hour faster than the other. Assuming that the first bus travels at a faster rate, then
x = y + 12
Recall that distance = speed × time.
The distance travelled by the first bus in 5 hours would be x × 5 = 5x
The distance travelled by the second bus in 5 hours would be y × 5 = 5y
the two buses are 750 miles apart after 5 hours. This means that total distance travelled by first bus and second bus in 5 hours is equal to 750 miles. Therefore,
5x + 5y = 750 - - - - - - - -- - 1
Substituting x = y + 12 into equation 1, it becomes
5(y+12) + 5y = 750
5y + 60 + 5y = 750
5y + 5y = 750 - 60
10y = 690
y = 690/10 = 69 miles per hour
x = y + 12 = 69 + 12
x = 81 miles per hour
