Question

Hans and Franz are two fitness fanatics. On a run from A to B, Hans runs half the way and walks the other half. Franz runs for half the time and walks for the other half. They both run at the same speed and walk at the same speed. who finishes first?

Answer 1

Interesting question.

Answer 2

Any ideas?

Answer 3

this one is confusing, if theyre both running and walkingat the same time wouldnt they both finish at the same time?

Answer 4

It's a little tricky.
Hans runs half the distance and walks half the distance, right?

Answer 5

right

Answer 6

Let's say he runs at twice the speed that he walks.
If it takes him 1 hour to walk half distance, then it takes him only 30 minutes to run the half distance. That means it takes him 1.5 hours to run & walk from A to B.

Answer 7

Ok so far?

Answer 8

yes good so far

Answer 9

Hans took 1.5 hours.
Notice that Hans walked an hour and ran 30 minutes.
He walked 2/3 of the total time, and ran 1/3 of the total time.

Answer 10

rok, right..

Answer 11

Now notice what Franz does. He runs half the time.
Hans ran 1/3 of the time, but Franz runs 1/2 of the time.
Franz spends a larger part of his time running which is faster than walking.

Answer 12

Shouldn't the time of their running and walking be EXACTLY the same?

Answer 13

No. The distance is the same, the times are different.

Answer 14

No the times should be the same too.

Answer 15

Also, they both walk at the same speed, and they also run at the same speed, but since Franz spends more time running, Franz gets there earlier.

Answer 16

They should spend the same amount walking and running.

Answer 17

i am a little confused now..

Answer 18

Franz and Hans -let's say they walk at 5 mph and run at 10 mph
let's say the distance is 2 miles
The time it takes EITHER to walk 1 mile is (1/5) of an hour = 12 minutes
The time it takes EITHER to run 1 mile is (1/10) of an hour = 6 minutes.

Answer 19

Since Hans spends 1/3 of his total time running, and Franz spend 1/2 of his total time running, Franz spent a larger part of his time at a higher speed, so Franz gets there first.

Answer 20

Why is the distance 4 miles and 2 miles for Franz.
They both run and walk the same distance

Answer 21

Notice the way the problem is stated.
Hans runs half the ___DISTANCE___ and walks half the ___DISTANCE___.
Franz runs half the ___TIME___ and walks half the ___TIME___.

Answer 22

Yes, they both end up running and walking the same combined distances, but Franz spends a larger percentage of his time running, so he finishes first.

Answer 23

It says Hans runs half the way ... Then says Franz runs half the time (it's worded badly !!)

Answer 24

way means distance.
time means time

Answer 25

yes - but it is still worded badly!!

Answer 26

distance would have been better than way.

Answer 27

Yes and better still if they didn't say runs the other half or walks the other half.

Answer 28

sorry if its worded badly that's how the problem is worded. @wolf1728