Question: A man can row upstream at 10 kmph and downstream at 20 kmph. Find the man's rate in still water and the rate of the stream.

Solution:

If a is rate downstream and b is rate upstream 

Rate in still water = (a + b)/2 

Rate of current = (a - b)/2 

Rate in still water = (20 + 10)/2 = 15 kmph 

Rate of current = (20 - 10)/2 = 5 kmph 

Question: A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is-

Solution: 

Let the length of the train is x m and speed is s.

ATQ,

s = (x + 800)/100 and,

s = (x + 400)/60

∴ (x + 800)/100 = (x + 400)/60

or, 60x + 48000 = 100x + 40000

or, 40x = 8000

or, x = 200 m

Question: A boat can travel 48 km upstream in 6 hours. If the speed of the stream is 2 km/hr, how much time will the boat take to cover a distance of 120 km downstream?

Solution:

Distance covered by a boat in 6 hours = 48 km

Rate upstream of boat = 48/6 

= 8 km/hr

Now,

Speed of stream = 2 km/hr

∴ Speed of boat in still water = (8 + 2)

= 10 km/hr

∴ Rate downstream of boat = (10 + 2) km/hr

= 12 km/hr

∴ Time taken in covering 120 km distance = 120/12 

= 10 hours