The two most important and only elements in this type of problems is a BOAT and a STREAM. A stream is nothing but the moving water, which is sometimes also called CURRENT.
In the question, by speed of the boat (or swimmer), we mean the speed of the boat (or swimmer) in still water.
Upstream:When the boat (or swimmer) moves against i.e. in the opposite direction of the stream.
Downstream:when the boat (or swimmer) moves in the same direction as that of the stream.
Now, if the speed of the boat is B km/hr while the speed of the stream is S km/hr, then
Upstream speed U = (B – S) km/hr
Downstream speed D = (B + S) km/hr
If in the question, you are provided with the upstream and the downstream speed U and D respectively, to determine the speed of boat and stream the formula goes like
Speed of boat B = (D + U) / 2
Speed of stream S = (D - U) / 2
Also, always have with you the basic speed formula,
Question: In still water, the speed of the boat is 7 km/hr. Find out the downstream speed of a boat in the river whose speed of the stream is 2 km/hr.
Solution: Downstream speed = Speed in still water + Speed of stream = 7 + 2 = 9 km/hr
A couple more formulae,
Formula 1:
If the ratio of downstream and upstream speeds is D : U, then ratio of time taken will be U : D.Question: 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?
Solution: When 8 hours 48 minutes is written using mixed fractions,
Therefore, the ratio of the time taken becomes
Which on solving gives,
Now, as the ratio of time is inversely proportional to that of Upstream and Downstream speeds.
Now, the ratio of speed of boat and the speed of stream will be
Formula 2:
When a boat’s speed in still water is B km/h and stream is flowing with a speed of S km/h and T is the time taken to row to a place and back, then the distance between the two places
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