### 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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