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a bus averages 2miles per hour faster than a motorcycle if the bus travels 165miles in the same time it takes the motorcyc

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A bus averages. 2miles per hour faster than a motorcycle. If the bus travels 165miles in the same time it takes the motorcycle to travel 155miles, then what is the speed of each?

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Answer to a math question A bus averages. 2miles per hour faster than a motorcycle. If the bus travels 165miles in the same time it takes the motorcycle to travel 155miles, then what is the speed of each?

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86 Answers

1. Let

v_m

be the speed of the motorcycle in miles per hour.
2. The speed of the bus is therefore

v_b = v_m + 2

miles per hour.
3. The time it takes for the motorcycle to travel 155 miles is

\frac{155}{v_m}

hours.
4. The time it takes for the bus to travel 165 miles is

\frac{165}{v_b}

hours.

Since these times are equal:

\frac{155}{v_m} = \frac{165}{v_b}

5. Substitute

v_b = v_m + 2

into the equation:

\frac{155}{v_m} = \frac{165}{v_m + 2}

6. Cross-multiply to solve for

v_m

:

155(v_m + 2) = 165v_m

155v_m + 310 = 165v_m

310 = 10v_m

v_m = 31

7. Therefore, the speed of the motorcycle is

v_m = 31

mph.
8. The speed of the bus is:

v_b = v_m + 2 = 31 + 2 = 33

mph

Answer:

v_m = 31 \text{ mph}, \quad v_b = 33 \text{ mph}

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