A boat covers a distance of 2.75 km upstream in 11 minutes. The ratio between speed of current and that of boat downstream is 1 : 7 respectively. The boat covers distance between A and B downstream in 52 minutes. What is the distance between point A and point B ?

Let speed of boat in still water = x kmph

Speed of current = y kmph

=> Rate upstream = $$(x - y)$$ kmph

and Rate downstream = $$(x + y)$$ kmph

=> $$\frac{y}{x + y} = \frac{1}{7}$$

=> $$7y = x + y$$

=> $$x = 6y$$

Again, $$\frac{2.75}{x - y} = \frac{11}{60}$$

=> $$x - y = \frac{60 * 2.75}{11}$$

=> $$6y - y = 15$$

=> $$y = \frac{15}{5} = 3$$kmph

and $$x = 6 * 3 = 18$$ kmph

Thus, rate downstream = 18 + 3 = 21 kmph

$$\therefore$$ Distance between points A & B = rate downstream * time

= $$21 \times \frac{52}{60} = 18.2$$ km