Find the rate of the rowing team in still water.

Question

A rowing team rowed 90 miles while going with the current in the same amount of time as it took to row 10 miles going against the current. The rate of the current was 4 miles per hour. Find the rate of the rowing team in still water.

Answer 1

1. let Rowing rate in still water = R
2. let current rate = C = 4 mph
3. Rowing with the current means the overall speed is R + C = R + 4
4. Rowing against the current means the overall speed is R - C = R - 4
5. Distance = Rate * Time
6. 90 = (R+4) * T   {Eqn 1}
7. 10 = (R-4) * T    {Eqn 2}
8. We have two unknowns (R& T) and two equations.  So, we can solve various ways.  May be easiest to solve simultaneously.  Subtract Eqn 2 from Eqn 1 after re-arranging.
1. 90/T = (R+4)
2. 10/T = (R-4)
3. 80/T = 8   {Subtracting 2nd line from first}
4. T = 80/8 = 10 hrs.
9. Now substitute the value of T back into Eqn 1, after re-arranging
1. 90/T - 4 = R
2. 90/10 - 4 = R
3. 9-4 = R
4. R = 5mph