Question

A sailor can row a boat 8 km downstream and return back to the starting point in 1hr 40mins . If the speed of the stream is 2km/h ,find the speed of the boat in still water.

Answer 1

Speed of stream=2 Km/h.Let speed of boat in still water be x Km/h. Time taken to travel downstream=8/(x+2). Time taken to travel upstream=8/(x-2). Total time=1 h 40 min=5/3 h. 8/(x+2)+8/(x-2)=5/3. 24(x-2)+24(x+2)=5(x+2) (x-2). 48x=5x^2-20. 5x^2-48x-20=0. x=48+√(-48)^2-4*5*(-20). x=48+√2304+400. x=48+52/10. x=100/10=10.Therefore speed of boat in still water=10km/h.

Answer 2

Answer:

Given;

Speed of the stream = 2km/h

Time taken = 1 hour 40 minutes = 5/3 h

Let the speed of the boat be x km/h.

A.T.Q.

(8/x+2) + (8/x-2) = 5/3

[8(x-2) + 8(x+2)]/(x+2)(x-2) = 5/3

(8x-16+8x+16)/x*2-4 = 5/3

3 × 16x = 5 (x*2-4)

5x*2-48x-20 = 0

5x*2-50x+2x-20 = 0

5x(x-10) +2(x-10) = 0

(5x+2)(x-10) = 0

5x+2=0 x-10=0

x= -2/5. x= 10

Speed of the boat in still water = 10 km/h