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In 40 seconds, a mountain biker travels 230 feet. What is her speed in miles per hour? (Note: 1 mile = 5280 feet)

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In 40 seconds, a mountain biker travels 230 feet. What is her speed in miles per hour? (Note: 1 mile = 5280 feet)

by Gmat_mission » Thu Aug 27, 2020 8:17 am

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In 40 seconds, a mountain biker travels 230 feet. What is her speed in miles per hour? (Note: 1 mile = 5280 feet)

A. \(\dfrac{230\cdot 60\cdot 60}{40\cdot 5280}\)

B. \(\dfrac{230\cdot 5280}{40\cdot 60\cdot 60}\)

C. \(\dfrac{40\cdot 60\cdot 60}{230\cdot 5280}\)

D. \(\dfrac{40\cdot 60\cdot 60\cdot 230}{5280}\)

E. \(\dfrac{40\cdot 60\cdot 60\cdot 5280}{230}\)

Answer: A

Source: Princeton Review
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Re: In 40 seconds, a mountain biker travels 230 feet. What is her speed in miles per hour? (Note: 1 mile = 5280 feet)

by dg1900 » Thu Aug 27, 2020 9:15 am
We can start the solution by stating speed in feet per second (use speed = distance/time). That would be
$$\frac{230}{40}$$ feet/second
We then convert it to feet/hour. To do this we multiply the numerator by 60. The reason behind this is that a person can travel 60 times the distance in an hour as compared to 1 second at the same speed.
So we get : $$\frac{230\cdot60}{40}$$ feet/hour
Now the final step is to convert to miles/hour. As 1 mile = 5280 feet we know a person can travel 1/5280 times the distance in feet at the same speed in the same given time. So we simply divide our previous answer by 5280. So our final answer is:
$$\frac{230\cdot60}{40\cdot5280}$$ miles/hour
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