Question 1114774: In 4 hours, Brooke can go 15 miles upriver and come back. The speed of the current is 5 mph.
Find the speed of the boat in still water.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Define the following variables:
b = speed of boat in still water
m = time it takes to go upriver
n = time it takes to go downriver
We're told it takes 4 hrs to go upriver and come back, so m+n = 4.
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Going upriver, you fight against the current, which means the boat speed is reduced by 5 mph as this is the current's speed
Therefore the rate is b-5
The equation to set up is...
distance = rate*time
d = r*t
15 = (b-5)*m
m = 15/(b-5)
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In contrast, if you go with the river or go downriver, then you add 5 mph onto the boat's speed in still water. So the rate is now b+5
d = r*t
15 = (b+5)*n
n = 15/(b+5)
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Recall earlier that m+n = 4
Plug the expressions found earlier for m and n into the equation m+n = 4
m+n = 4
15/(b-5)+15/(b+5) = 4
Now solve for b. We can multiply both sides by (b-5)(b+5) to clear out the fractions
15/(b-5)+15/(b+5) = 4
(b-5)(b+5) * [ 15/(b-5)+15/(b+5) ] = (b-5)(b+5) * 4
15(b+5)+15(b-5) = 4(b-5)(b+5)
15(b+5)+15(b-5) = 4(b^2-25)
15b+75+15b-75 = 4b^2-100
30b = 4b^2-100
4b^2-30b-100 = 0
Use the quadratic formula to solve for b and you'd find that
b = -5/2 or b = 10
Ignore the negative solution as it makes no sense to have a negative boat speed. The only practical answer is b = 10
The speed of the boat in still water is 10 mph.
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