In these type of situations, while calculating upstream speed we subtract the speed of river from the speed of boat because the river is pushing the boat downwards even when the boat is moving upwards. Whereas when the boat is moving downstream the speed is calculated by adding the speed of river to the speed of boat.
Let the speed of a boat ( or a body) in still water be x km/h and that of stream be y km/h, then
Let the speed of boat in downstream and upstream be u km/h and v km/h, then
Speed of boat in still water
Illustration: A boat goes downstream from one point to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream is 1 km/hr. Calculate the speed of boat in still water.
A. 15 Km/h B. 7.5 Km/h C. 19 Km/h D. 7 Km/h
Answer: C
Solution: Let the speed of boat in still water be x km/hr
Speed of stream = 1 km/hr
Speed upstream = x - 1 km/hr
Speed Downstream = x + 1 km/hr
As we know
Distance upstream = (x-1) X 10 = 10x - 10 Km
Distance Downstream = (x+1) X 9 = 9x + 9 Km
According to the question the distance is the same
10x-10 = 9x + 9
10x - 9x = 9+ 10
x = 19 km/hr
So the speed of boat in still water = 19 km/h
Hence the correct option is C.
Illustration: A motor boat whose speed in still water is 15 km/h, goes 40 km down stream and comes back in a total time of 6 hours. Find the speed of stream.
A. 5 Km/h B. 6 Km/h C. 15 Km/h D. 7 Km/h
Answer: A
A boat goes downstream from one point to another in 12 hours. It covers the same distance upstream in 15 hours. If the speed of the stream is 1 km/hr. Calculate the speed of boat in still water. | |||
Right Option : B | |||
View Explanation |
At his usual rowing speed. Kapil can travel 12 miles downstream in a certain river in 6 h less than he takes to travel the same distance upstream. But, if he could double his usual rowing speed for his 24 miles round trip, the downstream 12 miles would then take only 1 h less than the upstream 12 miles. What is the speed of the current ? | |||
Right Option : A | |||
View Explanation |
The current of a stream runs at 1 km/h. A motorboat goes 35 km upstream and back again at the starting point in 12 h. What is the speed of motorboat in still water ? | |||
Right Option : C | |||
View Explanation |
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