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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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?
Madelyn
4.788 Answers
1. Let v_m
2. The speed of the bus is therefore v_b = v_m + 2
3. The time it takes for the motorcycle to travel 155 miles is \frac{155}{v_m}
4. The time it takes for the bus to travel 165 miles is \frac{165}{v_b}
Since these times are equal:
\frac{155}{v_m} = \frac{165}{v_b}
5. Substitute v_b = v_m + 2
\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
8. The speed of the bus is:
v_b = v_m + 2 = 31 + 2 = 33
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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