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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Madelyn

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71 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}

2. The speed of the bus is therefore

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

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

Since these times are equal:

5. Substitute

6. Cross-multiply to solve for

7. Therefore, the speed of the motorcycle is

8. The speed of the bus is:

Answer:

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