A boat takes 51 minutes to go 10.2 km upstream. The ratio of the speed of the boat in still water to that of the stream is 7 : 6. How much total time (in hours) will the boat take to go 17.7 km upstream and 66.3 km downstream?​

Correct option is C

Given:

Time for 10.2 km upstream = 51 min = 0.85 h

Ratio u : v = 7 : 6 where (u) = speed of boat in still water, (v) = speed of stream

Required: time for 17.7 km upstream and 66.3 km downstream (in hours)

Formula Used:

Upstream speed = u - v ; Downstream speed = u + v

Time $$=\dfrac{\text{Distance}}{\text{Speed}}$$​​

Solution:

If u : v = 7:6

u = 7k, v = 6k

upstream = k, downstream =13k.

From the given upstream trip:
Upstream speed $$=\frac{10.2}{0.85}=12\ \text{km/h}\implies k=12.$$​​
Hence u = 7k = 84 km/h, v = 6k =72 km/h.
Downstream speed =13k=156 km/h.

Required times:

​$$t_{\text{up}}=\frac{17.7}{12}=1.475\ \text{h},$$​​

​$$t_{\text{down}}=\frac{66.3}{156}=0.425\ \text{h}.$$​​

Total time = 1.475 + 0.425 = 1.9 hours