Question

a thief after committee a theft runs at a uniform speed of 50 m/
minutes a policeman runs to catch him. he goes 60 m in first minute and increases his speed by 5m/minute every succeeding minute. after how many minutes the policeman will catch the thief?

Answer 1

Hey friend!!!

Here's ur answer...

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Let total time be n minutes.

Total distance covered = 50n meters.

Total distance covered by police man = 60 + 65 + 70....... + (n - 1) terms.

So,
$50n = \frac{n - 1}{2} (2(50) + (n - 1 - 1)5) \\ \\ 50n = \frac{n - 1}{2} (100 + 5n - 10) \\ \\ 100n = n - 1(90 + 5n) \\ \\ 100n = 90n + 5 {n}^{2} - 90 - 5n \\ \\ 5 {n}^{2} - 15n - 90 = 0 \\ \\ {n}^{2} - 3n - 18 = 0 \\ \\ {n}^{2} - 6n + 3n - 18 = 0 \\ \\ n(n - 6) + 3(n - 6) = 0 \\ \\ (n + 3)(n - 6) = 0 \\ \\ n = - 3(not \: possible) \\ n = 6 \: minutes. \\ \\ so \: time \: taken \: by \: policeman \: is \\ (n - 1) = 6 - 1 = 5 \: minutes.$

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Hope it may help you...

Thank you :) :))