IMAT 2017 Q13 [Running Speed]

Luke walks his puppy to a nearby park and lets the puppy off the lead.
As Luke starts walking along the path, the puppy runs on ahead, until it has gone 100 metres. The puppy then turns and runs back to Luke, who in that time has walked 50 metres. The puppy then goes on ahead again, turns after running 100 metres and runs back to Luke who has now walked another 50 metres.

This routine continues until Luke has walked 1 km.

If it takes 12 minutes for Luke to walk 1 km in the park, what is the puppy’s average running speed during the same time?

A. 12 km / h
B. 5 km / h
C. 10 km / h
D. 14 km / h
E. 15 km / h

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We are told that the puppy will run 100m and then back to Luke, who has walked 50m in that time.

How far does the puppy run in the time it takes Luke to go 50m?

So 100m out + 100m-50m back = 150m the puppy ran in the time Luke walks 50m

We know that Luke will go 1km total. 150m/50m = 3, so we know the puppy runs 3 times as far as Luke. The puppy therefore runs 3km in the time it takes Luke to do 1km, which is 12 minutes.

Now we need to find out the distance the puppy travels per hour:

\frac{60 min/h}{12min} (3km) = 15km/h
\fcolorbox{red}{grey!30}{Therefore E, 15km/h is correct}