MATH SOLVE

3 months ago

Q:
# Raft 16 miles with river current.at end of 16 miles turns around and rafts against river current. overall the journey takes 4 hours he can raft 9 mph in still water. what is speed of current

Accepted Solution

A:

Let the speed of the current of the river be = xAnd, the speed of the boat in still water = 9 mphThen, the speed of boat along the river current will be= 9+x mph
And, speed of boat against the river current will be = 9-x mphNow as given, total distance along river current and total distance against river current is same = 16 miles.As we know, time=distance/speedTime taken by boat along the river current = [tex]\frac{16}{9+x}[/tex]And time taken by boat against the river current = [tex]\frac{16}{9-x}[/tex]Also given is , the overall the journey takes 4 hours; so equation becomes[tex]\frac{16}{9+x}+\frac{16}{9-x}=4[/tex][tex]4(\frac{1}{9+x}+\frac{1}{9-x})=1[/tex]Solving this we get; [tex]x^{2} =9[/tex] or x=3Therefore, the speed of the current of the river is 3 mph.