SOLUTION: Two runners leave the starting gate, one running 12mph and the other 10mph. If they maintain the pace, how long will it take for them to be 1/4 mile apart?

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Question 156861This question is from textbook
: Two runners leave the starting gate, one running 12mph and the other 10mph. If they maintain the pace, how long will it take for them to be 1/4 mile apart? This question is from textbook

Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Two runners leave the starting gate, one running 12mph and the other 10mph. If they maintain the pace, how long will it take for them to be 1/4 mile apart?
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The difference in speed it 2 mph, so they separate at that rate.
1/4 mile at 2 mph will take 1/8 hour, or 7.5 minutes.

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Let's set up the equation for the faster runner:

Start with the distance-rate-time formula

Plug in

So after "t" hours, the faster runner has run miles
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Let's set up the equation for the slower runner:

Start with the distance-rate-time formula

Plug in

So after "t" hours, the faster runner has run miles

Now if you want to know the distance between them, simply subtract the two expressions to get

Since we want the distance to be of a mile, this means that

Start with the given equation.

Multiply both sides by the LCD to clear any fractions.

Distribute and multiply.

Combine like terms on the left side.

Divide both sides by to isolate .

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Answer:

So the answer is which approximates to .

So in of an hour (or 7 and half minutes) the distance between the two runners is of a mile