SOLUTION: The speed of the current in a river is 2 mph. Jay travels 20 miles upstream and 2o miles downstream in 5 1/3 hours. What is the speed of the boat?

Question 294619: The speed of the current in a river is 2 mph. Jay travels 20 miles upstream and 2o miles downstream in 5 1/3 hours. What is the speed of the boat?
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
D=RT
20=(R+2)T
T=20/(R+2) FOR THE TRIP DOWNSTREAM.
D=RT
20=(R-2)T
T=20/(R-2) FOR THE TRIP UPSTREAM.
ADD THE TWO TIMES.
20/(R+2)+20/(R-2)=5 1/3
[20(R+2)+20(R-2)]/(R+2)(R-2)=16/3
[20R+40+20R-40]/(R^2-4)=16/3 CROSS MULTIPLY.
16(R^2-4)=3(40R)
16R^2-64=120R
16R^2-12OR-64=0
8(2R^2-15R-8)=0
8(2R+1)(R-8)=0
R-8=0
R=8 MPH IS THE BOAT SPEED IN STILL WATER.
PROOF:
20/(8+2)+20/(8-2)=16/3
20/10+20/6=16/3
2+10/316/3
6/3+10/3=16/3
16/3=16/3
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