Question

A boat cover 32 km upstream and 36 km downstream in 7 hours . also ,it covers 40 km upstream and 48 km downstream in 9 hours . the speed of the boat in still water ?

Answer 1

Answer :

speed of still water=x

speed of stream=y

speed of boat upstream=(x-y)km/h

speed of boat down stream=(x+y)km/h

also, time = distance/speed

in first casewhen the boat goes32km upstream ,let the time taken, in hour be t1. then

t1= 32/x-y

let the t2 be the timetaken by the boat to go down stream

t2=36/x+y

so eq is 32/x-y +36/x+y=7

in second case the eq is

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

subsitute 1x-y=u ,1/x+y=v

so we get 32u +36v=7........... eq i

and 40u+48v=9

use elimination method to solve eq i and eq ii then we get,

v=1/12

u=1/8

1/x-y=u ,1/x-y=1/8

x-y =8 ..........eq 3

and x+y=12 eq 4

subtract both the eq we get

x=10

add both the eq we gt

y=2

so ,speed of stillwater is10km /h and stream is 2km/h