### Brain Teasers

# Jack & Jill

Jack and Jill are climbing down a vertical wall. They both use ropes hanging from the ceiling of a huge room. They start at the same time from the top of the wall which is 16 meters tall. The race is divided into two stages; the first 8 meters and the last 8 meters. A penalty of half a minute waiting time is placed upon whoever loses the first stage (first 8 meters) and it commences as soon as the winner finishes the first 8 meters.

The following describes their climbing techniques:

1. Jack climbs down in a zigzag way (moving one step downwards diagonally at a fixed angle from the horizon line). In each step movement he completes the distance of 1 meter diagonally. Initially, his feet are distant 60 cm apart aligned on a perfectly horizontal line. It takes him 15 seconds to complete each move. Jack has to rest for 1 minute for every 8 meters he vertically completes.

2. Jill hops down according to a perfect half circular arc movement. In each hop, she moves a distance of 1.57 meters along the arc path (not the vertical). It takes her 15 seconds to complete each hop. Jill has to rest for 1 minute for every 6 meters she vertically completes.

Who will reach the ground first and how many additional minutes will it take the loser to finish the race?

The following describes their climbing techniques:

1. Jack climbs down in a zigzag way (moving one step downwards diagonally at a fixed angle from the horizon line). In each step movement he completes the distance of 1 meter diagonally. Initially, his feet are distant 60 cm apart aligned on a perfectly horizontal line. It takes him 15 seconds to complete each move. Jack has to rest for 1 minute for every 8 meters he vertically completes.

2. Jill hops down according to a perfect half circular arc movement. In each hop, she moves a distance of 1.57 meters along the arc path (not the vertical). It takes her 15 seconds to complete each hop. Jill has to rest for 1 minute for every 6 meters she vertically completes.

Who will reach the ground first and how many additional minutes will it take the loser to finish the race?

### Answer

Jack will win the race and it will take an additional half minute to catch up with him.Jacks moves 0.8 meters vertically in each step movement:

According to Pythagoras theorem for right angled triangle:

A^2 = B^2+C^2 (where A is the hypotenuse)

Replacing A by the diagonally crossed distance, B by the distance between Jack's feet and C by the vertically climbed distance:

1^2 = 0.6^2+C^2

C = 0.8 m

Jill moves 1 meter vertically in each hop.

According to the circle circumference calculation:

Circumference = Diameter * Pi

(where Pi = 3.14 and Diameter is the vertically climbed down distance)

2 * 1.57 = D * 3.14

Diameter = 1 meter

1.Time: 1.5 minutes elapsing

Jack: Finished 4.8 meters

Jill: Finished 6.0 meters and starting her 1 minute rest

2.Time: 2.5 minutes elapsing

Jack: Finished 8.0 meters (crossed an additional 3.2 meters in 1 minute while Jill is resting)

Jill: Finished 6.0 meters and ending her 1 minute rest

Note: Losing the first stage (8 meters), Jill has to wait for half minute penalty time and at the same time Jack starts his 1 minute rest having crossed 8.0 meters.

3. Time: 3.0 minutes elapsing

Jack: Finished 8.0 meters and still resting for another half a minute

Jill: Finished 6.0 meters and resuming her climb down having finished the half

minute penalty

4.Time: 3.5 minutes elapsing

Jack: Finished 8.0 meters and ending his 1 minute rest

Jill: Finished 8.0 meters (crossed an additional 2.0 meters in half minute while Jack is resting)

5. Time: 4.5 minutes elapsing

Jack: Finished 11.2 meters

Jill: Finished 12.0 meters and starting her 1 minute rest

6.Time: 5.5 minutes elapsing

Jack: Finished 14.4 meters (crossed an additional 3.2 meters in 1 minute while Jill is resting)

Jill: Finished 12.0 meters and ending her 1 minute rest

7.Time: 6.0 minutes elapsing

Jack: Finishing the race (16 meters) as the winner

Jill: Finished 14.0 meters and needing another two meters to finish the race which will take her an additional half minute

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## Comments

I know this comment might make me sound jealous or even dumb, but don't you think this was just a tab bit to elaborate

I just wanted to make sure all details are given, no elaboration was intended, yet, thanks for the input.

Something's wrong when it's harder to read the question than answer it.

Uh, what about having his feet 60cm apart determines the angle Jack climbs at?

I had to assume that was the horizontal distance he moved since there was no other information to use, but WHY it was 60cm based on his foot position was a mystery. Overall a poorly worded and somewhat tedious teaser.

I had to assume that was the horizontal distance he moved since there was no other information to use, but WHY it was 60cm based on his foot position was a mystery. Overall a poorly worded and somewhat tedious teaser.

I agree with Java. The wording does not make it clear that the initial 60 cm Jacks feet are apart determines the horizontal component of each of his steps. Apart from that I thought it was a good teaser.

I made it through the title before giving up anyways.

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