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A lighthouse is located at A …

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A lighthouse is located at A 2 km off shore from the nearest point o on a straight beach and a shop is located at B of the beach at a distance of 4 km from O if the housekeeper can row with motor boat at the speed of 4 km/h and can walk at the rate of 6 km/h where should he plan to reach the shore so as to cover the distance to the shop in the least possible time ?

Posted by Riya Bansal 7 years, 9 months ago

CBSE > Class 12 > Mathematics

1 answers

Kalindi Yadav 7 years, 9 months ago

Draw a right angled triangle AOB, AO=2km,OB= 4 km.And OB is the sea shore and A is the lighthouse. The housekeeper starts from A, so he can take two paths From A to O, then O to B. In this path he will take 2/6 +4/4 = 1.33 hr Another path is the hypotenuse AB, the hypotenuse is always short from the sum of two sides of right triangle. Hence AB = √20 So this distance will be totally covered by motor boat Hence the time taken is 20√6hr Hence this is the minimum time taken by the house keeper to reach the shop.

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