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# Park leaves home for work and drives at 30mph. 20 mins later Susan realizes he left his tool box at home. If she drives at 40 mph,?

how far she drives before she overtakes him? Correct answer is 40. Can somebody please explain how to get to the answer?

### 2 Answers

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- Jeff AaronLv 76 years agoFavorite Answer
Assuming they took the same route:

x hours after Susan leaves, she has driven 40x miles

Since Park left 20 minutes earlier, that's 1/3 of an hour earlier, so he has driven for x + (1/3) hours, so he has driven 30(x + (1/3)) = 30x + 10 miles.

When they meet:

40x = 30x + 10

40x - 30x = 10

10x = 10

x = 10/10

x = 1

So Susan has driven for 1 hour, so she drove 40*1 = 40 miles.

- DavidLv 76 years ago
In 20 minutes, Park will have gone 10 miles. There is a 10 miles per hour differential in speed. That means every four minutes, Susan catches up 1 mile. To overtake the 10 mile advantage, take 4x10. QED

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