  Question 17

# A motorboat takes the passengers from Rishikesh to Haridwar and back. Both the cities, Rishikesh and Haridwar are located on the banks of River Ganga. During Kumbh Mela,to earn more money, the owner of the motorboat decided to have more trips from Rishikesh to Haridwar and back, so he increased the speed of the motorboat in still water, by 50%. By increasing the speed, he was able to cut down the travel time from Rishikesh to Haridwarand back, by 60%. Whatis the ratio of the speed of motorboating still water to that of the speed of river Ganga?

Solution

Let the speed of the boat in the still water = 100x and the travel time = 100t and the distance between Rishikesh and Haridwar be 'd'

Let the speed of the river be 100r

Since the owner of the motorboat decides to increase the number of trips, he increased the speed.

Increased speed in still water = 150x

Final travel time = 40t

$$\ \frac{\ d}{100x+100r}+\ \frac{\ d}{100x-100r}=100t$$   ---(1)

After the ease in speed

$$\ \frac{\ d}{150x+100r}+\ \frac{\ d}{150x-100r}=40t$$     ---(2)

Dividing 1 by 2, we get x/r = $$\sqrt{\ \ \frac{\ 11}{6}}$$