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Chapter 7: Problem 13

In 40 seconds, a mountain biker travels 230 feet. What is her speed in miles per hour? (Note: 1 mile \(=5280\) feet) $$ \begin{array}{r} \frac{230 \times 60 \times 60}{40 \times 5280} \\ \frac{230 \times 5280}{40 \times 60 \times 60} \\ \frac{40 \times 60 \times 60}{230 \times 5280} \\ \text { I don't know. } \end{array} $$

Short Answer

Expert verified
The correct option is \(\frac{230 \times 60 \times 60}{40 \times 5280}\). It represents the speed of the mountain biker in miles per hour.

Step by step solution

01

Understanding the conversion ratios

Recognize that 1 mile equals 5280 feet. Thus, to convert feet to miles, you can divide the number of feet by 5280. Similarly, there are 60 seconds in a minute and 60 minutes in an hour, so to convert seconds to hours, you would divide the number of seconds by 3600 (60*60).
02

Convert distance from feet to miles

The mountain biker travels 230 feet, which needs to be converted into miles by dividing by 5280. Hence, the distance in miles can be calculated as: \[ Distance = \frac{230}{5280} \] miles.
03

Convert time from seconds to hours

The biker has taken 40 seconds. To convert this into hours, you divide by 3600. This gives: \[ Time = \frac{40}{3600} \] hours.
04

Calculate speed in miles per hour

Speed is calculated as distance divided by time. Therefore, the speed of the mountain biker in miles per hour is: \[ Speed = \frac{Distance}{Time} = \frac{\frac{230}{5280}}{\frac{40}{3600}} \]
05

Simplify the expression

Simplify the fraction to get the speed of the mountain biker in miles per hour. This will be the final answer.

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