Question 185061: please help me solve this word problem thank you.
junior's boat will go 15 miles per hour in still water. If he can go 12 miles
downstream in the same amount of time as it takes to go miles upstream, then what is the speed of the current.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443)   (Show Source):
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Your problem statement left out an important detail:
"[J]unior's boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go ??? miles upstream, then what is the speed of the current[?]"
However, all is not lost.
Remember that distance equals rate times time, that is:
Which, for this problem, will be convenient to express as:
Let the speed of the current be represented by  and your missing upstream distance be represented by m.
When the boat is going downstream, the boat is actually moving the speed through still water plus the speed of the current. When going upstream, it is the speed in still water minus the speed of the current.
For the downstream trip, which we know to be 12 miles, we can write:
For the upstream trip, which we are saying is m miles, we can write:
Now remembering that the problem said the amount of time for the downstream and upstream trips was the same, we can equate the two right sides of the above equations:
Giving us a proportion. Step 1: Cross-multiply:
 = m(15 + r_c))
Step 2: Simplify, collect terms, and solve for :
 = 180 - 15m)
Step 3: Once you determine the correct value for m you can substitute and do the arithmetic to determine .
John
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