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- Identify upstream or downstream.
- Apply the correct effective speed.
- Use distance/time relation.
Correct Answer: B
Correct Answer: B
Method / Topic: Boats and Streams
The answer uses the correct effective speed of the boat.
Short Explanation
Detailed Explanation
Correct Answer: B
Method / Topic: Boats and Streams
Use the standard Boats and Streams relations as required:
Downstream speed = speed in still water + stream speed.
Upstream speed = speed in still water - stream speed.
Speed in still water = (downstream speed + upstream speed)/2.
Stream speed = (downstream speed - upstream speed)/2.
Also use Speed = Distance / Time and Time = Distance / Speed wherever required.
For equal time, downstream/upstream speed = 72/48 = 3/2. Thus (15+x)/(15-x)=3/2, giving x=3 km/h.
CHECK:
Substituting the obtained values back into the downstream/upstream relations or the distance-time relation reproduces the given data and the selected option.
EXAM TIP:
First identify whether the motion is downstream or upstream. For equal distances, time is inversely proportional to speed. For given downstream and upstream speeds, use their average for boat speed and half their difference for stream speed.
Do not add the stream speed for upstream motion or subtract it for downstream motion. Also do not confuse a time ratio with a speed ratio for equal distances; the ratios are inverse.
PRACTICAL EXAMPLE:
A river current assists a boat moving downstream and opposes it upstream, so the same boat has two different effective speeds.
Therefore, the correct
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Shortcut used, common trap, and the fastest solving route
- Identify upstream or downstream.
- Apply the correct effective speed.
- Use distance/time relation.
The speed of a boat in still water is 15 km/h. It covers 72 km downstream in the same time in which it covers 48 km upstream. Find the speed of the stream.
Explanation
Correct Answer: B
Method / Topic: Boats and Streams
The answer uses the correct effective speed of the boat.
Short Explanation
Detailed Explanation
Correct Answer: B
Method / Topic: Boats and Streams
Use the standard Boats and Streams relations as required:
Downstream speed = speed in still water + stream speed.
Upstream speed = speed in still water - stream speed.
Speed in still water = (downstream speed + upstream speed)/2.
Stream speed = (downstream speed - upstream speed)/2.
Also use Speed = Distance / Time and Time = Distance / Speed wherever required.
For equal time, downstream/upstream speed = 72/48 = 3/2. Thus (15+x)/(15-x)=3/2, giving x=3 km/h.
CHECK:
Substituting the obtained values back into the downstream/upstream relations or the distance-time relation reproduces the given data and the selected option.
EXAM TIP:
First identify whether the motion is downstream or upstream. For equal distances, time is inversely proportional to speed. For given downstream and upstream speeds, use their average for boat speed and half their difference for stream speed.
Do not add the stream speed for upstream motion or subtract it for downstream motion. Also do not confuse a time ratio with a speed ratio for equal distances; the ratios are inverse.
PRACTICAL EXAMPLE:
A river current assists a boat moving downstream and opposes it upstream, so the same boat has two different effective speeds.
Therefore, the correct
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