SOLUTION: From a point on a river, two boats are driven in opposite directions, one at 5 miles per hour, and the other at 8 miles per hour. In how many hours will they be 52 miles apart?

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Question 166479: From a point on a river, two boats are driven in opposite directions, one at 5 miles per hour, and the other at 8 miles per hour. In how many hours will they be 52 miles apart?
(This question is from a sample MET. Thanks very much.)
Found 2 solutions by vleith, gonzo:
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
They are moving away from each other at a rate of =
How many hours will it take to go 52 miles if you are going 13 mph?

Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website!
D = R * T (distance = rate * time)
let x = distance boat 1 travels at 5mph in one direction.
let y = distance boat 2 travels at 8mph in the opposite direction.
total distance traveled by both boats = 52 miles.
x + y = 52 (equation 1)
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boat 1 travels x miles at 5 mph in T hours.
boat 2 travels y miles at 8 mph in T hours.
since R * T = D,
x = 5*T (equation 2)
y = 8*T (equation 3)
if you add equation 2 and 3 together, you get
x + y = 13*T (equation 4)
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you have 2 equations that you need to solve simultaneously. they are:
x + y = 52 (equation 1)
x + y = 13*T (equation 4)
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subtract equation 1 from equation 4:
you get:
0 = 13*T - 52
add 52 to both sides:
52 = 13*T
divide both sides by 13:
T = 4
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they will be 52 miles apart in 4 hours.
to prove, substitute in equations 2 and 3:
x = 5*4 = 20 miles
y = 8*4 = 32 miles
20 + 32 = 52
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answer is proven.
they are 52 miles apart in 4 hours.
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