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Two boats A and B start towards each other from two places, 150 km apart. Speed of the boat A and B in still water are 16 km/hr and 14 km/hr respectively. If A proceeds down and B up the stream, they will meet after.
- a)4.5 hours
- b)4 hours
- c)5 hours
- d)6 hours
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Two boats A and B start towards each other from two places, 150 km apa...
Let the speed of the stream be x kmph and both the boats meet after t hours.
According to the question,
Distance covered while going downstream + Distance covered while going upstream = Total Distance
⇒ (16 + x) t + (14 – x) t = 150
⇒ 16t + 14t = 150
⇒ 30t = 150
⇒ t = 5 hrs
Hence, option C is correct.
According to the question,
Distance covered while going downstream + Distance covered while going upstream = Total Distance
⇒ (16 + x) t + (14 – x) t = 150
⇒ 16t + 14t = 150
⇒ 30t = 150
⇒ t = 5 hrs
Hence, option C is correct.
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Community Answer
Two boats A and B start towards each other from two places, 150 km apa...
Given Information:
- Distance between boats A and B = 150 km
- Speed of boat A in still water = 16 km/hr
- Speed of boat B in still water = 14 km/hr
Approach:
1. Determine the relative speed of the boats.
2. Use the formula Time = Distance/Speed to calculate the time taken for the boats to meet.
3. Compare the calculated time with the given options to find the correct answer.
Calculation:
1. Relative Speed:
- When boat A proceeds downstream, its effective speed is increased by the speed of the stream.
- When boat B proceeds upstream, its effective speed is decreased by the speed of the stream.
- The speed of the stream is the difference between the speeds of boat A and B in still water.
- Speed of the stream = Speed of boat A - Speed of boat B = 16 km/hr - 14 km/hr = 2 km/hr
2. Time taken to meet:
- The boats are moving towards each other, so their relative speed is the sum of their individual speeds.
- Relative speed = Speed of boat A + Speed of boat B = 16 km/hr + 14 km/hr = 30 km/hr
- Time taken to meet = Distance/Relative speed = 150 km/30 km/hr = 5 hours
3. Comparison with options:
- The calculated time is 5 hours, which matches with option (c).
Therefore, the correct answer is option (c) - 5 hours.
- Distance between boats A and B = 150 km
- Speed of boat A in still water = 16 km/hr
- Speed of boat B in still water = 14 km/hr
Approach:
1. Determine the relative speed of the boats.
2. Use the formula Time = Distance/Speed to calculate the time taken for the boats to meet.
3. Compare the calculated time with the given options to find the correct answer.
Calculation:
1. Relative Speed:
- When boat A proceeds downstream, its effective speed is increased by the speed of the stream.
- When boat B proceeds upstream, its effective speed is decreased by the speed of the stream.
- The speed of the stream is the difference between the speeds of boat A and B in still water.
- Speed of the stream = Speed of boat A - Speed of boat B = 16 km/hr - 14 km/hr = 2 km/hr
2. Time taken to meet:
- The boats are moving towards each other, so their relative speed is the sum of their individual speeds.
- Relative speed = Speed of boat A + Speed of boat B = 16 km/hr + 14 km/hr = 30 km/hr
- Time taken to meet = Distance/Relative speed = 150 km/30 km/hr = 5 hours
3. Comparison with options:
- The calculated time is 5 hours, which matches with option (c).
Therefore, the correct answer is option (c) - 5 hours.
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Question Description
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