Quantitative Aptitude Boats and Streams Study Material
Upstream : If a person/swimmer, boat or ship moves against the stream i.e., in the direction opposite to that of the stream, it is called upstream.
Downstream: If a person/swimmer, boat or ship moves with the stream i.e., along the direction of the stream, it is called downstream.
Assumption : When we simply say speed of the boat or swimmer, it usually means speed in the still water.
Let the speed of the boat or swimmer in still water be Z km/hr and the speed of the stream or the current be S km/hr
Then the boat or the swimmer has
Down stream Speed = (Z+ S) km/hr
Up stream Speed = (Z – S) km/hr .
On adding the above two relationships and dividing by 2 we get.
Speed of the boat in still water 1/2 [Downstream Speed + Upstream Speed]
Similarly, on subtracting and dividing by 2 we get,
Speed of the stream =1/2 [Downstream Speed – Upstream Speed]
(i) Speed in still water is equal to half the sum of Up-stream Speed and Downstream Speed.
(ii) Speed of the stream is equal to half the difference of Downstream Speed and Upstream Speed.
Ex.1. The speed of a boat in still water is 15 km/hr. If the speed of the stream be 3 km/hr, find its downstream and upstream speeds.
Sol. Speed of the boat in still water (Z) = 15 km/hr
Speed of the stream (S) = 3 km/hr
Downstream speed= Z+S=(15 + 3)km/hr =18km/hr
Upstream speed=Z-S = (15-3)km/hr= 12km/hr
Ex. 2. A man can row downstream at 16 km/hr and up¬stream at 10 km/hr. Find his speed in still water and the rate of the current.
Sol. Speed in still water 1
= 1/2 [Downstream Speed + Upstream Speed]
= 1/2 [16+10] km/hr
= 13 krn/hr Rate of the current
= 1/2 [Downstream Speed – Upstream Speed]
= 1/2 [16-10] km/hr
= 3 km/hr A ns.
Ex. 3. A man swims downstream 40 km in 4 hours and upstream 24 km in 3 hours. Find his speed in still water and also the speed of the current
Sol. Downstream speed = 40/4 = 10 km/hr
Upstream speed = 24/3 = 8 km/hr
Speed in still water= 1/2 (10 + 8) = 9 km/hr.
Speed of the current= 1/2 (10 – 8) = 1 km/hr
Ex. 4. The speed of a boat in still water is 12 km/hr. It takes twice as long to go upstream to a point as to return downstream to the starting point. What is the speed of the current?
A man rows a certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of the stream be 5 km/hr, then his speed in still water is given by
A man can row a boat in still water at Z km/hr. In a stream flowing at S km/hr if it takes him t hours to row to a point and come back, then the distance (D) between the two points is
Ex. 5. The speed of a boat in still water is 12 km/hr. It takes 6 hours to row’ a certain distance and return to the starting point in a river flowing at 4 km/hr. Find the distance