SOLUTION: A boat can go 10 miles against the current in the same it can go in 30 miles with the current. The current flows at 4 mph. Find the speed of the boat in no current.

Question 109824: A boat can go 10 miles against the current in the same it can go in 30 miles with the current. The current flows at 4 mph. Find the speed of the boat in no current.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let r=rate (speed) of the boat with no current
Now we know that:
(r-4)=rate against the current
(r+4)=rate with the current
distance(d)=rate(r) times time(t) or d=rt; t=d/r and r=d/t
Time required to go 10 miles against the current=10/(r-4)
Time to go 30 miles with the current=30/(r+4)
----And we are told that the above two times are equal. So our equation to solve:
10/(r-4)=30/(r+4) multiply both sides by (r-4)(r+4) or cross-multiply and we get:
10(r+4)=30(r-4) get rid of parens (distributive law)
10r+40=30r-120 subtract 10r from and add 120 to both sides
10r-10r+40+120=30r-10r-120+120 collect like terms
160=20r divide both sides by 20
r=8 mph-------------------------------boat's rate of speed with no current
CK
10/(8-4)=30/(8+4)
10/4=30/12
10/4=10/4
Hope this helps---ptaylor
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