Question

John rows his boat 10km down a river and 10km back to his original point of departure. If his rowing speed is 5k(m)/(h) in still water and thelotal times for his journey is 5 hours, what is the speed of the river current? (Answer to 2 decimal places )

Answer 1

Answer: Vw = 2.23 km/h

Explanation:

(V0 + Vw)t1 = d

(V0 - Vw)t2 = d

t = t1 + t2

where d = 10 km and t = 5 h

From the first three equations we have:

d/(V0 + Vw) + d/(V0 - Vw) = t ( I inserted t1 and t2 into the third equation)

(d(V0 - Vw) + d(V0 + Vw)) / V0² - Vw² = t

(dV0 - dw + dVo + dVw) / Vo² - Vw² = t

(2×d×V0) = t(V0² - Vw²)

`Vw = \sqrt{(tV0^(2) -2dV0)/(t) }`

`Vw = \sqrt{5`

Vw = 2.23 km/h