Boats and Streams :

1. The speed of a boat in still water is 40 km/hr. If the speed of the stream be 8 km/hr, find its downstream and upstream speeds.

Solution : Speed of the boat (X)=40 km/hr

Speed of the stream (Y) = 8 km/hr

∴ Downstream speed = X+Y=(40+8) = 48 km/hr

and, upstream speed = X−Y=(40−8) = 32 km/hr

2. A boat is rowed down a river 80 km in 10 hours and up a river 42 km in 14 hours. Find the speed of the boat and the river.

Solution : Speed of the boat downstream = 80/10=8 km/hr

Speed of the boat upstream = 42/14 = 3 km/hr

∴ Speed of the boat

= ½( Downstream speed + upstream speed)

= ½(8+3) =11/2= or 5.5 km/hr

and, speed of the river

= ½( Downstream speed − upstream speed)

= ½(8−3) =5/2= or 2.5 km/hr

3. A man rows at a speed of 9 km/hr in still water to a certain distance upstream and back to the starting point in a river which flows at 6 km/hr. Find his average speed for total journey.

Solution : Average speed

= Upstream × downstream/ Man’s rate in still water

= (9−6) (9+6)/9=5 km/hr

4. A man can rows 14 km/hr in still water. If the river is running at 6 km/hr, it takes 12 hours more in upstream than to go downstream for the same distance. How far is the place.

Solution : The required distance

=(X²−Y²) t/2Y

=(196−36) 12/2×6

=160 km/hr

5. A motor boat cover a certain distance downstream in 12 hours but takes 16 hours to return upstream to the starting point. If the speed of the stream be 12 km/hr, find the speed of the motor boat in still water.

Solution : Speed of the motorboat in still water

= Y(t2+t1/t2−t1) km/hr

= 12(16+12/16−12)=84 km/hr.