## Saturday, August 11, 2018

### Boat & Stream

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find  the time taken by the boat to go 68 km downstream.
Speed downstream = (13 + 4) km/hr = 17 km/hr.
 Time taken to travel 68 km downstream = 68 hrs = 4 hrs. 17

A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:

Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr.
Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr.
A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
Let the man's rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.  x x 8 4 = (y x 4) 5 44 x =4y 5 y = 11 x. 5 Required ratio = y + x : y - x 2 2
 = 16x x 1 : 6x x 1 5 2 5 2
 = 8 : 3 5 5
= 8 : 3.
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is: 30 + 30 = 4 1 (15 + x) (15 - x) 2 900 = 9 225 - x2 2 9x2 = 225 x2 = 25 x = 5 km/hr.