If a boatman rows his boat 35km up stream and 55km downstream in 12 hours and he can row 30km upstream and 44 km downstream in 10hr, then the speed of the stream and that of the boat in still water

To solve this problem, let us assume linear motion so that we can use the equation:

t = d / v

where t is time, d is distance and v is velocity

First let us assign some variables, let us say that the velocity upstream is Vu while Velocity downstream is Vd, so that:

35 / Vu + 55 / Vd = 12 - - - > 1

30 / Vu + 44 / Vd = 10 - - - > 2

We rewrite equation 1 in terms of Vu:

(35 / Vu + 55 / Vd = 12) Vu

35 + 55 Vu / Vd = 12 Vu

12 Vu - 55 Vu / Vd = 35

Vu (12 - 55 / Vd) = 35

Vu = 35 / (12 - 55 / Vd) - - - > 3

Also rewriting equation 2 to in terms of Vu:

Vu = 30 / (10 - 44 / Vd) - - - > 4

Equating 3 and 4:

35 / (12 - 55 / Vd) = 30 / (10 - 44 / Vd)

35 (10 - 44 / Vd) = 30 (12 - 55 / Vd)

Multiply both sides by Vd:

350 Vd - 1540 = 360 Vd - 1650

10 Vd = 110

Vd = 11 km / h

Using equation 3 to solve for Vu:

Vu = 35 / (12 - 55 / 11)

Vu = 5 km / h

Answers:

Vu = 5 km / h = velocity upstream

Vd = 11 km / h = velocity downstream