B starts 4.5 minutes after A from the same point, for a place at a distance of 3.5 miles from the starting point. A on reaching the destination turns back and walk a mile where he meets B. If A’s speed is a mile in 6 minutes then B’s speed is a mile in _minutes?
Question
B starts 4.5 minutes after A from the same point, for a place at a distance of 3.5 miles from the starting point. A on reaching the destination turns back and walk a mile where he meets B. If A’s speed is a mile in 6 minutes then B’s speed is a mile in _minutes?
Solution
To solve this problem, we need to follow these steps:
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First, we need to calculate the time it takes for A to reach the destination. Since A's speed is a mile in 6 minutes, and the destination is 3.5 miles away, A will take 3.5 miles * 6 minutes/mile = 21 minutes to reach the destination.
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A then turns back and walks a mile before meeting B. This takes an additional 6 minutes (since A's speed is a mile in 6 minutes), so A has been walking for a total of 21 minutes + 6 minutes = 27 minutes.
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However, B started 4.5 minutes after A, so when A and B meet, B has been walking for 27 minutes - 4.5 minutes = 22.5 minutes.
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At the point where A and B meet, B has walked 2.5 miles (since the meeting point is a mile away from the destination and the destination is 3.5 miles from the start).
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Therefore, B's speed is 2.5 miles / 22.5 minutes = 0.1111 miles/minute.
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To convert this to minutes per mile (as the question asks for B's speed in minutes per mile), we take the reciprocal of 0.1111 miles/minute, which gives us approximately 9 minutes/mile.
So, B's speed is a mile in approximately 9 minutes.
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