SOLUTION: A Johnson motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at 2mph, find the speed of the boat in still water.

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: A Johnson motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at 2mph, find the speed of the boat in still water.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 987007: A Johnson motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at 2mph, find the speed of the boat in still water.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
More general:
A Johnson motorboat goes d%5Bu%5D miles upstream in the same time it requires to go d%5Bd%5D miles downstream. If the river flows at s mph, find the speed r of the boat in still water. 
Direction         rate     time    distance
upstream          r-c       t      d%5Bu%5D
downstream        r+c       t      d%5Bd%5D


Direction         rate       time    distance
upstream          r-c       d%5Bu%5D%2F%28r-c%29      d%5Bu%5D
downstream        r+c       d%5Bd%5D%2F%28r%2Bc%29      d%5Bd%5D



The time quantities were described as equal.
highlight_green%28d%5Bu%5D%2F%28r-c%29=d%5Bd%5D%2F%28r%2Bc%29%29
Their reciprocals are also equal (not the only strategy)...
%28r-c%29%2Fd%5Bu%5D=%28r%2Bc%29%2Fd%5Bd%5D
%28r-c%29d%5Bd%5D=%28r%2Bc%29d%5Bu%5D
r%2Ad%5Bd%5D-c%2Ad%5Bd%5D=r%2Ad%5Bu%5D%2Bc%2Ad%5Bu%5D
rd%5Bd%5D-rd%5Bu%5D=cd%5Bu%5D%2Bcd%5Bd%5D
r%28d%5Bd%5D-d%5Bu%5D%29=cd%5Bu%5D%2Bcd%5Bd%5D
highlight%28r=%28cd%5Bu%5D%2Bcd%5Bd%5D%29%2F%28d%5Bd%5D-d%5Bu%5D%29%29

Evaluate the boat speed r according to
system%28d%5Bu%5D=5%2Cd%5Bd%5D=7%2Cc=2%29.

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

A Johnson motorboat goes 5 miles upstream in the same time it requires to go 7 miles downstream. If the river flows at 2mph, find the speed of the boat in still water.
Let speed of boat in still water be S

Then total speed upstream (boat in still water, less speed of river current) = S - 2

Total speed downstream (boat in still water, plus speed of river current) = S + 2

We then get: 5%2F%28S+-+2%29+=+7%2F%28S+%2B+2%29

7(S - 2) = 5(S + 2) -------- Cross-multiplying

7S - 14 = 5S + 10

7S - 5S = 10 + 14

2S = 24

S, or speed of boat in still water = 24%2F2, or highlight_green%2812%29 mph