Question: A train 250 meters long is running at a speed of 90 km/h. How long will it take to cross a platform 150 meters long?

Solution:

speed = 90 km/h = 90 × (5/18) m/s

= 25 m/s

To cross the platform have to travel = (250 + 150) m

= 400 m

∴ Required time = 400/25 seconds

= 16 seconds

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 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