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?Options₹ 8₹ 10₹ 12₹ 9
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?Options₹ 8₹ 10₹ 12₹ 9
Solution
The problem can be solved in the following 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, it will take A 6 * 3.5 = 21 minutes to reach the destination.
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Then, A turns back and walks a mile. This will take an additional 6 minutes, so A has been walking for a total of 21 + 6 = 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 - 4.5 = 22.5 minutes.
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At the time they meet, A has walked 3.5 miles to the destination and 1 mile back, for a total of 4.5 miles. B, on the other hand, has walked less than 3.5 miles. The difference is the 1 mile that A walked back, so B has walked 3.5 - 1 = 2.5 miles.
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To find B's speed, we divide the distance B has walked by the time B has been walking. So, B's speed is 2.5 miles / 22.5 minutes = 0.111 miles per minute.
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To convert this to minutes per mile, we take the reciprocal, so B's speed is 1 / 0.111 = 9 minutes per mile.
So, the answer is ₹ 9.
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