Two friends 6 km apart walk towards each other at 4 km/h and 5 km/h. Their dog starts with one of them and runs back and forth between them at 12 km/h until the friends meet. How far does the dog run in all?

8 kmCorrect answerYour answer12 kmCorrect answerYour answer14.4 kmCorrect answerYour answer18 kmCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The friends meet after $\frac{6}{4+5} = \frac{2}{3}$ h.
The dog runs non-stop for that whole time.
Dog's distance $= 12 \times \frac{2}{3} = 8$ km.

Worth noting

There is no need to add up the separate legs: the dog's running time equals the friends' meeting time. 18 km wrongly uses 1.5 h, the time the slower friend alone would need for the whole 6 km.

Concept: Using total time rather than summing a series of legs
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsRelative speed

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Ten questions from Time, Speed & Distance, at your own pace.

Two friends 6 km apart walk towards each other at 4 km/h and 5 km/h. Their dog starts with one of them and runs back and forth between them at 12 km/h until the friends meet. How far does the dog run in all?

Explanation