• 0

# Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

• 0

important 5 mark board question

Share

### 1 Answer

1. Given: Speed of boat in still water = 15 km/hr.

Let the speed of stream = x km/hr.

Distance covered by boat in going upstream = Distance covered by boat in downstream = 30 km

Speed of boat upstream = Speed of boat in still water â€“ Speed of stream = (15 – x) km/hr.

Speed of boat downstream = Speed of boat in still water + Speed of stream = (15 + x) km/hr.

Since, Distance = Speed Ã— Time

â‡’Â Time = Distance / Speed

Time taken by boat upstream =Â

Time taken by boat downstreamÂ

Total time taken by the boat to go and come back to the same point = 4.5 hrs.

âˆ´Â

Multiply and divide both sides by (15 – x)(15 + x):

â‡’Â 4.5 (225 â€“ x2) = 30(15 + x) + 30(15 – x)

â‡’Â 1012.5 â€“ 4.5x2Â = 450 + 30x + 450 â€“ 30 x

â‡’Â 1012.5 â€“ 4.5x2Â = 900

â‡’Â 4.5x2Â = 112.5

â‡’Â x2Â = 25

â‡’Â x =Â Â 5

But speed canâ€™t be negative,Â âˆ´Â Speed of the stream = 5 km/hr.

• 0