Question

the time taken by boat to row it 5 km downstream is same as rowing it 3 km upstream. if the speed of the stream had been half km/h more, the speed of the boat downstream would have been double it's speed upstream. find thenspeed of boat in still water and speed of the stream.​

this is question of liner equation in two variable

Answer 1

Hey Dear,

◆ Answer -

vr = 1.5 km/h

vb = 6 km/h

● Explaination -

Let, vb be speed of boat and vr be speed of river.

Speed of the boat upstream would be -

vu = vb - vr

Therefore, distance covered in time t,

su = vu × t

3 = (vb-vr)t ...(1)

Speed of the boat downstream would be -

vd = vb + vr

Therefore, distance covered in time t,

sd = vd × t

5 = (vb+vr)t ...(2)

From (1) & (2),

(vb+vr) / 5 = (vb-vr) / 3

3vb + 3vr = 5vb - 5vr

2vb = 8vr

vb = 4vr ...(3)

If vb have been half km/h more,

vb - (vr+0.5) = 2 [vb + (vr+0.5)]

vb - vr - 0.5 = 2vb + 2vr + 1

vb = 3vr + 1.5 ...(4)

Putting vb = 4vr,

4vr = 3vr + 1.5

vr = 1.5 km/h

Now, substituting

vb = 4vr = 4×1.5

vb = 6 km/h

Therefore, speed of the boat in steady water is 6 km/h and speed of river stream is 6 km/h.

Best luck...