Question

A boat goes 80 km upstream and 120 km downstream in 20 hours. In 15 hours, it can go 48 km upstream and 108 km downstream. Determine the speed of the boat in still water and that of the stream.

Answer 1

Let speed of boat be x & speed of stream be y

Hence upstream speed = x- y = u

Downstream speed = x+ y = v

$t_{11}$ = time taken downstream in first case

$t_{12}$ = time taken upstream in first case

$t_{21}$ = time taken downstream in second case

$t_{22}$ = time taken upstream in second case

now,

$t_{11}$ + $t_{12}$ = 20

i.e. $\frac{120}{v}$ + $\frac{80}{u}$ = 20 then $\frac{6}{v}$ + $\frac{4}{u}$ = 1&

$t_{21}$ ​+ $t_{22}$ ​= 15

$\frac{108}{v}$ + $\frac{48}{u}$ = 15 then $\frac{36}{v}$ + $\frac{16}{u}$ = 5

Solving we get v = 12 & u = 8

Hence x = 10 & y = 2