# How far does the dog walk?

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Mahendra walks up and down a hill which is three kilometers each way. His dog, being slower, walks at half the speed. When Mahendra reaches the top of the hill he turns around and walks down to meet his dog part way. Mahendra continues walking to the bottom of the hill maintaining his speed. The dog follows him, also maintaining his speed.

How far does the dog walk?

posted Aug 14, 2015

Let speed of mahendra be 1km/hr.
then his dog's speed will be 0.5km/hr.
Mahendra will reach the top of the hill(3 kms)in 3 hrs.
By that time his dog would have reached 1.5 km.
Then he turns around and walks down 1 km for 1 hr .
By that time his dog would have reached another 0.5km.That point will be located 2 km from bottom and 1 km from the top.
In that point mahendra meet his dog.
after that the dog follows mahendra to reach the bottom.
Totally the dog walks 4km. Ans is 4 Km

Mahendra and dog meet at a point which is L (km) from origin after T hours. Mahendra speed is S (km/hour) and dog S/2 (km/h)
So, Dog walks S/2 x T = L (km).....(1) and Mahendra walks S x T = 3+ (3-L) = 6 - L (km) ......(2)
From (1) and (2) we get L = 2 km. So dog walks 2 x L = 4 km

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