Explanation Formula used: Distance travelled is equal to speed × time . Calculation: Let at time t both the ships are nearest to each other, distance travelled D 1 by Ship A. Substitute, Speed = 18 km/hr and Time = t in above formula D 1 = 18 t . Distance travelled D 2 by Ship B. Substitute, Speed = 16 km/hr and Time = t in above formula D 2 = 16 t . Then, distance between both the ships D , D 2 = D 1 2 + D 2 2 D = D 1 2 + ( 40 − D 2 ) 2 Substitute, D 1 2 = 18 t and D 2 2 = 16 t in D = D 1 2 + ( 40 − D 2 ) 2 . D = D 1 2 + ( 40 − D 2 ) 2 = ( 18 t ) 2 + ( 40 − 16 t ) 2 = 324 t 2 + 1600 + 256 t 2 − 1280 t = 580 t 2 − 1280 t + 1600 Differentiate D with respect to t . D = 580 t 2 − 1280 t + 1600 d D d t = 1160 t − 1280 580 t 2 − 1280 t + 1600 ( 1 2 ) = 580 t − 640 ( 580 t 2 − 1280 t + 1600 ) For maxima and minima d D d t = 0 . 580 t − 640 ( 580 t 2 − 1280 t + 1600 ) = 0 580 t − 640 = 0 580 t = 640 t = 1

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Chapter 24.7, Problem 21E

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The time, while the ships are nearest each other.

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Chapter 24.7, Problem 20E

Chapter 24.7, Problem 22E

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