SOLUTION: I have spent hours on this one and been through every one I know Can you help? Please? Upstream Downstream Jr's boat will go 15 miles per hour in still water. If he can go 12

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Question 152187: I have spent hours on this one and been through every one I know Can you help? Please?
Upstream Downstream
Jr's boat will go 15 miles per hour in still water. If he can go 12 miles down stream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current. T= D/R... D = RT .. R = D/T

Found 2 solutions by ankor@dixie-net.com, mducky2:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jr's boat will go 15 miles per hour in still water. If he can go 12 miles down stream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current.
:
Let x = speed of the current
then
(15+x) = boat speed downstream
and
(15-x) = boat speed up stream
:
Times are equal so write a time equation; Time = Dist/speed
:
Downstream time = Upstream time
12%2F%28%2815%2Bx%29%29 = 9%2F%28%2815-x%29%29
Cross multiply and you have:
9(15+x) = 12(15-x)
:
135 + 9x = 180 - 12x
:
9x + 12x = 180 - 135
:
21x = 45
x = 45%2F21
x = 2.143 mph speed of the current
;
:
Check solution by finding the time of each
(12/17.143) = (9/12.857)
.69999 ~ .70000; because x actually = 2.142877143

Answer by mducky2(62) About Me  (Show Source):
You can put this solution on YOUR website!
If we think of the stream as a conveyor belt, the current is carrying the boat at the same time that the boat is going 15 mph. In other words, the upstream distance really means the distance that the boat traveled plus the distance the water traveled. The same logic goes for downstream:
Dboat + Dcurrent = 12
Dboat - Dcurrent = 9

If we subtract the bottom equation from the top equation:
Dboat - Dboat + Dcurrent + Dcurrent = 12 - 9
2Dcurrent = 3
Dcurrent = 1.5

Plugging this back into the first equation:
Dboat + 1.5 = 12
Dboat = 10.5

Since we know that the current and the boat traveled a certain distance in the same amount of time, we can equate the time of the boat to the time of the current:
T = (Dboat/Rboat) = (Dcurrent/Rcurrent)

We can plug in the numbers that we know:
Dboat = 10.5 miles
Rboat = 15 mph
Dcurrent = 1.5 miles
Rcurrent = C

Now we can solve for the rate of the current
(Dboat/Rboat) = (Dcurrent/Rcurrent)
10.5/15 = 1.5/C
C = (1.5*15)/10.5
C = 2.143

Therefore, the speed of the current is 2.143 mph.