Question

A boat takes 128 minutes lesser to travel to 48 km downstream than to travel the upstream in the same distance.The speed of the boat is 3 km/hr.What is the speed of the boat in still water?

Answer 1

Let speed of boat in still water is X .

time take by boat to 48km upstream is t
__________________ downstream is T

Speed of downstream=X+3
Speed of upstream = X-3

t (Upstream)= 48/(X-3)
T (downstream) =48/ (X+3)

According To Question

t - T = 128/60

$\frac{48}{x - 3} - \frac{48}{x + 3} = \frac{128}{60} \\ \frac{48x + 144 - 48x + 144}{(x - 3)(x + 3)} = \frac{32}{15}$

288 /(X^2 -9) = 32/15

Or,X^2-9 = 15×9

Or,X^2=144

X=12

So the speed of boat in still water is 12 kmph.


Verification

48/15 = 16/5×60 = 192 minutes

48/ 9= 16/3 ×60= 320 minutes


Difference in time taken= 320-192=128

Verified