SOLUTION: From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 6 miles per hour. In how many hours will they be 32 miles apart?

Question 126355: From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 6 miles per hour. In how many hours will they be 32 miles apart?
If anyone could help that would be great!
thanks
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let =distance first boat travels and =distance second boat travels

Let's find the equation for the distance the first boat travels

Start with the distance-rate-time formula

Plug in and

So the first equation is

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Let's find the equation for the distance the second boat travels

Start with the distance-rate-time formula

Plug in and

So the second equation is

Now since we want to know when the two boats will be 32 miles apart, the total distance both boats travel is 32 miles. In other words, the sum of and is 32. So we have the third equation

Plug in and

Combine like terms on the left side

Divide both sides by 16 to isolate t

Divide

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Answer:
So our answer is

So in 2 hours, the two boats will be 32 miles apart

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