Judy drove $20$ miles from her house to a theater at an average rate of $50$ miles per hour. Greg drove from his house to the theater in $1/3$ of the time it took Judy to drive to the theater, and they both arrived at the theater at the same time. If Judy left her house at 7:30 P.M., when did Greg leave his house?

- 7:34 P.M.
- 7:38 P.M.
- 7:42 P.M.
- 7:46 P.M.
- 7:54 P.M.

So, you were trying to be a good test taker and practice for the GRE with PowerPrep online. Buuuut then you had some questions about the quant section—specifically question 13 of the second Quantitative section of Practice Test 1. Those questions testing our knowledge of **Ratios and Proportions** can be kind of tricky, but never fear, PrepScholar has got your back!

## Survey the Question

Let’s search the problem for clues as to what it will be testing, as this will help shift our minds to think about what type of math knowledge we’ll use to solve this question. Pay attention to any words that sound math-specific and anything special about what the numbers look like, and mark them on our paper.

Ah, this looks like one of those distance-rate-time type of questions. We know that they require us to use our knowledge of **Ratios and Proportions**. Let’s keep what we’ve learned about this skill at the tip of our minds as we approach this question.

## What Do We Know?

Let’s carefully read through the question and make a list of the things that we know.

- Judy’s trip to the theater was $20$ miles, driven at an average of $50$ miles per hour
- Greg’s trip to the theater took $1/3$ as much time as Judy’s trip
- Judy and Greg both arrived at the theater at 7:30 P.M.
- We want to know what time Greg left to travel to the theater

## Develop a Plan

For distance-rate-time questions, we have the formula:

$$\Distance = \Rate · \Time$$

From the details given in this question, we can see a solution path that will lead to the time that Greg left his house.

- Using $20$ miles as a distance and $50$ miles per hour as a rate, calculate how many hours it took Judy to drive to the theater
- Convert Judy’s trip time from hours to minutes by multiplying by $60$
- Take the time of Judy’s trip and divide it by $3$ to get Greg’s trip time
- Add Greg’s trip time in minutes to 7:30 P.M. to get the time that Greg left his house

With this plan in place, let’s finish solving this question!

## Solve the Question

First, let’s find the time, in hours, of Judy’s trip

$$\Time = {\Distance}/{\Rate} = 20 / 50 = 0.4 \hours$$

Now, let’s multiply this time by $60$ to convert it to minutes

$$0.4 \hours ·({60 \minutes} / {1 \hour}) = 24 \minutes$$

Excellent job so far. Now if we know that Judy’s trip took $24$ minutes and Greg’s trip was $1/3$ of Judy’s trip time, then Greg’s trip took $24/3$ minutes, or $8 \minutes$.

We also know that if Judy left at 7:30 P.M. and her trip took $24$ minutes, then she must have arrived at the theater at 7:54 P.M. If Greg’s trip was $8$ minutes long and he arrived at the theater at 7:54 P.M. (since they both arrived at the same time) then he must have left his house $8$ minutes before 7:54 P.M., or at 7:46 P.M.

**The correct answer is D, 7:46 P.M**.

## What Did We Learn

Well, that was definitely quite involved for what at first seemed like a simple distance-rate-time question. Breaking the question down into smaller bits and solving each part separately definitely made it more manageable.

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