A boat takes 39 minutes to go 27.9 km upstream. The ratio of the speed of the boat in still water to that of the stream is 9 : 4. How much total time (in hours) will the boat take to go 18.9 km upstream and 51.3 km downstream?​

Correct option is B

Given:

Time taken to go 27.9 km upstream = 39 minutes

Speed ratio of boat in still water to stream = 9 : 4

Distance to travel upstream = 18.9 km

Distance to travel downstream = 51.3 km

Solution: 

Let speed of boat = 9x and speed of stream = 4x  

The boat takes 39 minutes to go 27.9 km upstream:

Time for upstream = $$\frac{\text{Distance}}{\text{Speed}} = \frac{27.9}{5x}$$​

Given that the time taken is 39 minutes:

​$$\frac{27.9}{5x} = 39 \text{ minutes}$$​

​$$\frac{27.9}{5x} = \frac{39}{60}$$​​

​$$\frac{27.9}{5x} = 0.65$$​​

​$$27.9 = 0.65 \times 5x$$​​

27.9 = 3.25x

x = $$\frac{27.9}{3.25}$$​ = 8.58

Upstream speed = 5x = 5 × 8.58 = 42.9 km/h

Downstream speed = 13x = 13 × 8.58 = 111.54 km/h

Time upstream = $$\frac{18.9}{42.9}$$​ = 0.441 hours

Time downstream = $$\frac{51.3}{111.54}$$​ = 0.460  hours

Total time = 0.441 + 0.460 = 0.901 hours = 0.90 hours