a boat goes 24km upstream and 28km downstream in 6hrs . it goes 30km upstream and 21 km downstream in 6 1/2 hrs . find the speed of boat in still water and also speed of stream

Hemasri Rajendiran
From Gems Our Own English High School, added an answer, on 24/5/14

67 helpful votes in Math
let the speed of the boat in still water be x km/hr and speed of the current be y km/hr

speed of the boat in upstream = (x-y) km/hr

speed of the boat in down stream = (x+y) km/hr

since time = distance / speed

it goes 24km upstream and 28 km down stream in 6 hours.

therefore

it goes 30km upstream and 21km downstream in 6 1/2 hrs. i.e. 13/2 hrs therefore

let

eq (1) and eq(2) becomes:

multiplying eq(1)' by 3 and subtracting eq(2)' :

put u = 1/6 in eq(1)' ;

therefore

adding eq(3) and eq(4):

subtracting eq(3) from eq(4):

thus the speed of the boat in still water is 10km/hr and speed of the current is 4km/hr

hope this helps you.

cheers!!

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