If Vishal covers 184 km in a boat in 48 hours against the stream and he takes 12 hours with the stream, then find the speed of the stream.​

Correct option is D

Given:

Distance D = 184 km.

Time downstream t$$_d$$​ = 12 h → downstream speed v$$_d = \dfrac{184}{12}$$​ km/h.

Time upstream t$$_u$$​ = 48 h → upstream speed v$$_u = \dfrac{184}{48}$$​ km/h.

If boat speed in still water = b, stream speed = s: $$v_d =$$ b + s, v$$_u =$$​ b - s.

Formula Used:

v =$$\dfrac{D}{t}.$$​​

​$$s = \dfrac{v_d - v_u}{2} \\ \ \\ b = \dfrac{v_d + v_u}{2}$$​​

Solution:
​$$v_d = \dfrac{184}{12} = \dfrac{46}{3}$$​ km/h,

​$$v_u = \dfrac{184}{48} = \dfrac{23}{6}$$​ km/h.

Stream speed
s$$=\frac{v_d-v_u}{2}$$​​

=$$\frac{\frac{46}{3}-\frac{23}{6}}{2}$$​

=$$\frac{\frac{92-23}{6}}{2}$$​

=$$\frac{69}{12}=\frac{23}{4}=5.75\ \text{km/h}.$$​​

The speed of the stream is 5.75 km/h.

​