Question

A man walking his dog along a Straight road spots a friend a mile away. They wave at one another and the dog sprints to greet her. As soon as the dog arrives it turns around and runs straight back to its master. Then turns around again and runs back to the girl, who is, of course, nearer now. The dog continues running backs and forth until the two meet. Given that each person walks at a steady 3 mph, and the dog runs a steady 9 mph, what is the total distance the dog runs?

Answer 1

The distance the dog runs is given by the time it takes the man and the

girl to meet multiplied by the speed of the dog.

Correct response:

• The total distance the dog runs is 1.5 miles

How to find the distance ran by the dog

Given parameters;

Initial distance of the friend away = 1 mile

Speed of the man = 3 mph

Speed of the girl = 3 mph

Speed of the dug = 9 mph

Required:

The total distance the dog runs

Solution:

$Time = \mathbf{\dfrac{Distance}{Speed}}$

The time it takes the man and the girl to meet, t, is given as follows;

$t = \dfrac{1 \ mile}{3 \ mph + 3 \ mph} = \mathbf{\dfrac{1}{6} \, hours}$

Therefore;

• $The \ total \ distance \ dog \ runs, \ d = 9 \ mph \times \dfrac{1}{6} \, hours = \underline{ 1.5 \, miles}$

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