# Question 43427

Apr 20, 2015

It's important to understand what Downstream and Upstream mean here.

Let's assume the Speed of the Boat in Still water to be ${S}_{b}$ and the speed of the current to be ${S}_{c}$(which is 4kmph )

color(green)(*Downstream would mean that the current and the boat are moving in the SAME direction . Hence the speed of the current would enhance the speed of the boat and the overall speed would be ${S}_{b} + {S}_{c}$

We know that $T i m e = \frac{D i s \tan c e}{S p e e d}$

For Downstream it will be
color(green)(Time(Downstream) = 40 / (S_b + S_c) = 40 / (S_b + 4)

color(red)(*Upstream would mean that the current and the boat are moving in the OPPOSITE direction . Hence the speed of the current would restrict the speed of the boat and the overall speed would be ${S}_{b} - {S}_{c}$

For Upstream it will be
color(red)(Time(Upstream) = 24 / (S_b - S_c) = 24 / (S_b - 4)

• Based on the data given,

color(green)(Time(Downstream) = color(red)(Time(Upstream)

$\frac{40}{{S}_{b} + 4} = \frac{24}{{S}_{b} - 4}$

$40 \left({S}_{b} - 4\right) = 24 \left({S}_{b} + 4\right)$

$40 {S}_{b} - 160 = 24 {S}_{b} + 96$

$40 {S}_{b} - 24 {S}_{b} = 96 + 160$

$16 {S}_{b} = 256$

${S}_{b} = 16$

The rate of Jai Singh’s boat in still water will be color(blue)(16 kmph#