The time taken by a boat to travel 75 km upstream is equal to 1$$\frac 23$$of  the time it takes to travel 60 km downstream. The speed of the boat in still water is 28 km/h. How much time (in hours) will the boat take to travel 51.2 km downstream?

Correct option is C

Given :

Distance upstream = 75 km

Distance downstream = 60 km

Speed of boat in still water = 28 km/h

Time upstream = $$1 \dfrac{2}{3} = \dfrac{5}{3}$$ of time downstream

Required distance downstream = 51.2 km

Formula Used :
Speed upstream = (b - s), Speed downstream = (b + s)
​$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$​​

Solution :

Let speed of stream = s km/h

Upstream speed = (28 - s)
Downstream speed = (28 + s)

Given condition:
​$$\frac{75}{28 - s} = \frac{5}{3} \times \frac{60}{28 + s}$$​​

​$$\frac{75}{28 - s} = \frac{100}{28 + s}$$​​

75(28 + s) = 100(28 - s)

2100 + 75s = 2800 - 100s

175s = 700
s = 4

Downstream speed:
= 28 + 4 = 32 km/h

Time to travel 51.2 km downstream:
​$$= \frac{51.2}{32} = 1.6 \text{ hours}$$​​