Question
A bus averages 2 miles per hour faster than a motorcycle. If the bus travels 165 miles in the same time it takes the motorcycle to travel 155 miles, then what is the speed of each?
A bus averages 2 miles per hour faster than a motorcycle. If the bus travels 165 miles in the same time it takes the motorcycle to travel 155 miles, then what is the speed of each?
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Koala Tutor
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Let the speed of the motorcycle be x miles per hour.
Then the speed of the bus is x+2 miles per hour.
The time taken by the motorcycle to travel 155 miles is 155/x hours.
The time taken by the bus to travel 165 miles is 165/(x+2) hours.
As both the times are equal, we can equate them:
155/x = 165/(x+2)
Cross multiplying, we get:
155(x+2) = 165x
155x + 310 = 165x
10x = 310
x = 310/10
x = 31
Therefore, the speed of the motorcycle is 31 miles per hour.
The speed of the bus is 31+2 = 33 miles per hour. Answer: \boxed{31,33}.
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