SOLUTION: A city bus finishes it 96 mile route in the same the same amount of time that a rural bus finishes its 144 mile route. The city bus averages 18mph slower than the rural bus how lon

Algebra ->  Proportions -> SOLUTION: A city bus finishes it 96 mile route in the same the same amount of time that a rural bus finishes its 144 mile route. The city bus averages 18mph slower than the rural bus how lon      Log On


   

Question 1057860: A city bus finishes it 96 mile route in the same the same amount of time that a rural bus finishes its 144 mile route. The city bus averages 18mph slower than the rural bus how long does it take each bust to finish its route
Answer by solve_for_x(190) About Me  (Show Source):
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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%2F%28x-18%29+=+144%2Fx

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.