Question 123524
An express bus travels 320 miles in the same amount of time that a car travels 280 miles. The rate of the car is 8 mph less that the rate of the bus. Find the rate of the bus.
:
Let s = the rate of the bus
then
(s-8) = rate of the car
:
Write a time equation: Time = {{{Distance/Rate}}}
:
Bus time = Car time
{{{320/s}}} = {{{280/((s-8))}}}
Cross multiply:
:
320(s-8) = 280s 
:
320s - 2560 = 285s
:
320s - 280s = +2560
:
40s = 2560
s = {{{2560/40}}}
s = 64 mph is the bus
:
:
Check our solution by find the times (are they equal)
Car speed 64 - 8 = 56 mph
320/64 = 5 hrs
280/56 = 5 hrs confirms our solution