SOLUTION: If a boat can do 10 miles per hour in still water and takes the same time to go 12 miles up stream as 15 down stream find the speed of the current.

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Question 885614: If a boat can do 10 miles per hour in still water and takes the same time to go 12 miles up stream as 15 down stream find the speed of the current.
Found 2 solutions by josmiceli, lwsshak3:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = the speed of the current
Let +c+ = the rate of the current in mi/hr
Let +t+ = elapsed time in hrs
-------------------
Going upstream:
(1) +12+=+%28+10+-+c+%29%2At+
Going downstream:
(2) +15+=+%28+10+%2B+c+%29%2At+
-------------------------
(1) +12+=+10t+-+c%2At+
(2) +15+=+10t+%2B+c%2At+
Add the equations:
+27+=+20t+
+t+=+27%2F20+
+t+=+1.35+ hrs
and
(1) +12+=+%28+10+-+c+%29%2A1.35+
(1) +10+-+c+=+12%2F1.35+
(1) +-c+=+-10+%2B+8.8889+
(1) +c+=+1.111+
The speed of the current is 1.111 mi/hr
--------------------
check:
(2) +15+=+10t+%2B+c%2At+
(2) +15+=+10%2A1.35+%2B+1.111%2A1.35+
(2) +15+=+13.5+%2B+1.5+
(2) +15+=+15+
OK

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If a boat can do 10 miles per hour in still water and takes the same time to go 12 miles up stream as 15 down stream find the speed of the current.
***
let x=speed of current
10+x=speed of boat downstream
10-x=speed of boat upstream
travel time=distance/speed
..
12%2F%2810-x%29=15%2F%2810%2Bx%29
12(10+x)=15(10-x)
120+12x=150-15x
27x/30
x=30/27=10/9
speed of the current=10/9 mph