Question

1. claire is digging a hole for a fence post. so far, she has dug \\(\frac{4}{10}\\) of the hole in \\(\frac{1}{4}\\) of an hour. she continues to dig at the same rate. how many minutes will it take her to dig the entire hole? 37.5 minutes

Explanation:

Step1: Find the rate of digging

The rate is the fraction of the hole dug per hour. She dug $\frac{4}{10}$ of the hole in $\frac{1}{4}$ hour. So the rate $r$ is $\frac{\frac{4}{10}}{\frac{1}{4}}=\frac{4}{10}\times\frac{4}{1}=\frac{16}{10}=\frac{8}{5}$ of the hole per hour.

Step2: Find time to dig 1 hole

Let $t$ be the time in hours to dig 1 hole. Since rate $\times$ time = work (1 hole), $t = \frac{1}{r}=\frac{1}{\frac{8}{5}}=\frac{5}{8}$ hours.

Step3: Convert hours to minutes

Since 1 hour = 60 minutes, $\frac{5}{8}\times60=\frac{300}{8}=37.5$ minutes.

Answer:

37.5 minutes