A boat can travel 5 km upstream in 15 minutes. If the ratio of the speed of the boat in still water to the speed of the stream is 6 : 1, then how much time will the boat take to cover 19.6 km downstream?

If the ratio of the speed of the boat in still water to the speed of the stream is 6 : 1. 

Let's assume the speed of boat in still water and the speed of the stream are '6y' and 'y' respectively.

A boat can travel 5 km upstream in 15 minutes.

$$speed\ in\ upstream = \frac{distance}{time}$$

$$6y-y=\frac{5}{\frac{15}{60}}$$ [Here 15 is divided by 60 because we need to convert minutes into hours]

$$5y=\frac{5}{\frac{1}{4}}$$

y = 4

Time taken by the boat to cover 19.6 km downstream = $$\frac{distance}{speed\ in\ downstream}$$

= $$\frac{19.6}{6y+y}$$

= $$\frac{19.6}{7y}$$

Put the value of 'y'.

= $$\frac{19.6}{7\times4}$$

= $$\frac{19.6}{28}$$

= 0.7 hours

As we know that 1 hour = 60 minutes.

0.7 hours = $$60\times0.7$$ minutes

= 42 minutes