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

The answer is 7:46 PM.

I can only find Judy's time of arrival at the theatre, which is 0.4 hr or 24 minutes. What do I do next?

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    add it to $7:30$ so that you can know the arrival time. Then subtract $24/3$ to this result. – 2017-01-31

1 Answers 1

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Greg took $1/3$ of Judy's time, or a third of $24$ minutes, which means Greg took $8$ minutes to get to the theater.

Now, we also know that Judy took $24$ minutes to get to the theater and she left at $7:30$ PM, so she arrives at the theater at $7:54$ PM.

Subtract $8$ minutes from this to get $7:46$, which is when Greg left the house.