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?

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Let d%5B1%5D=distance first boat travels and d%5B2%5D=distance second boat travels



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

d=rt Start with the distance-rate-time formula


d%5B1%5D=10t Plug in d=d%5B1%5D and r=10


So the first equation is d%5B1%5D=10t


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

d=rt Start with the distance-rate-time formula


d%5B2%5D=6t Plug in d=d%5B2%5D and r=6


So the second equation is d%5B2%5D=6t




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 d%5B1%5D and d%5B2%5D is 32. So we have the third equation


d%5B1%5D%2Bd%5B2%5D=32


10t%2B6t=32 Plug in d%5B1%5D=10t and d%5B2%5D=6t



16t=32 Combine like terms on the left side


t=%2832%29%2F%2816%29 Divide both sides by 16 to isolate t



t=2 Divide

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Answer:
So our answer is t=2



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