Question

A boat covers 32 km upstream and 30 km downstream in 7 hours. It also covers 40 km upstream and 48 km downstream in 8 hours. Find the speed of the boat in still water and the speed of the stream.

Answer 1

Let the speed of the boat in still water = x km/hr

speed of steam = y km/hr

upstream speed =x + y

downstream speed =x - y

So, according to question ---

the eqution will be -

32/x-y + 36/x+y = 7 and

40/x-y + 48/x+y=9

by taking 1/x-y=u and 1/x+y=v

32u+36v=7

40u+48v=9

32u+36v=7*10

40u+48v=9*8

320u+360v=70

320u+384v=72

-24v=-2

hence v=1/12

put value of v in eq

40u+48*1/12=9

40u=9-4

u=5/40

u=1/8

now 1/x-y=1/8 => x-y =8

and 1/x+y=1/12 => x+y = 12

hence x= 10 km/hr and y = 2km/hr.

HOPE IT HELPS YOU IN ANSWERING YOUR QUESTION