Question 1057860
Let x represent the speed of the rural bus.


The speed of the city bus is then represented by x - 18.


The time that each bus travels is calculated by dividing the distance by the speed.


The time that the city bus takes is: 96 / (x - 18)


The time that the rural buss takes is 144/x


Since the times are the same we can write:


{{{96/(x-18) = 144/x}}}


This can be rearranged as:


96x = 144(x - 18)


96x = 144x - 2592


96x - 144x = -2592


-48x = -2592


x = -2592 / -48


x = 54 miles per hour


The time required is then:


144 / x = 144 / 54 = 2.67 hours


Each bus takes 2.67 hours to complete its route.