Rate

[Guest]

A man rows his boat across a lake and back in 2.5 hours. The rate returning was 2 mph less than going. Total distance- 12 miles. Calculate rate each way.


Rate * Time = Distance
Distance/Time = Rate



X- RATE OF GOING
X-2 RATE OF RETURN

RATE TIME DISTANCE

GOING X 6

RETURN X-2 6

TOTAL 2.5 12


12/2.5 = 4.8

4.8-2 = 2.8

That is not correct. Where did I make the error(s)?

[Guest]

Let X = outward speed
Then X-2 = return speed

(6/X) + (6/(X-2) = 2.5
(12/X) + (12/(X-2) = 5
12X - 24 + 12X = 5X^2 - 10X
5X^2 - 34X + 24 = 0
(X - 0.8)(5X - 30) = 0

then...X = 0.8 OR X = 6

So outspeed is 6mph and returnspeed is 4mph