College Algebra

Question

A bus averages 6 miles per hour faster than a trolley. If the bus travels 90 miles in the same time it takes the trolley to travels 75 miles, then what is the speed of each?

Answer 1

Let x = speed of trolley in mph. Then x+6= speed of bus in mph.

90/(x+6) = the time in hours for the bus to go 90 miles

75/x = the time in hours for the trolley to go 75 miles. The problem states that the two times are the same, so

90/(x+6) = 75/x. Cross multiply to get 75(x+6) = 90x.

Expand to get 75x + 450 = 90x. Subtract 75x from both sides to get 450 = 15x. Divide by 15 to get

x= 30 mph for the trolley, so x+6 = 36 mph for the bus

Answer 2

Since the bus travels 6 mph faster and traveled 15 miles further in a particular amount of time, that time was 15/6 or 2.5 hours. So, the bus' speed is 90/2.5 or 36 mph while the trolly's is 75/2.5 or 30 mph.