# Ian runs 0.18 miles a minute. How many minutes will it take Ian to run 4.23 miles?

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1
Feb 6, 2018

Ian runs 0.18 miles a minute

Speed of Ian $= \text{Distance"/"Time" = "0.18 mile"/"1 minute" = "0.18 mile/min}$

Time taken for Ian to run 4.23 miles is
$\text{Time" = "Distance"/"Speed" = "4.23 miles"/"0.18 mile/min" = "23.5 min}$

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Feb 6, 2018

23.5 minutes

#### Explanation:

The problem states that in one minute, Ian will travel .18 miles. The problem is asking you to identify the time it takes for Ian to complete 4.23 miles. What the problem has given is two distance values and a time value. The easiest way to understand this problem is by setting up this ratio:

$\frac{1}{.18} = \frac{x}{4.23}$

Next, cross multiply:

$4.23 = .18 x$

Finally, solve for x by dividing both sides by .18

$23.5 = x$

This works because we assume Ian's rate never changes as he runs. Therefore, no matter how far he runs, whether it be a fraction of a mile or a million miles, his miles per minute will remain constant. If we set the unknown value over the desired distance equal to the miles per minute ratio we were given (we were told in one minute, Ian runs .18 miles), we can find the minutes it takes for Ian to run 4.23 miles, or x.

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