Question

We have a 50 ft piece of rope. If it takes one second to cut it into a one-foot piece. How long would it take to cut the entire rope into one-foot pieces?

Answer 1

Given:

50 ft piece of rope.

It takes 1 second to cut it into a one-foot piece.

To find:

Total time taken to cut the entire rope into one - foot pieces = ?

Solution:

Let us consider the length of rope left and time taken after each cut.

In 1st cut, time taken is 1 second, the rope will be 49 ft left.

In 2nd cut, total time taken is 2 seconds, the rope will be 48 ft left.

In 3 seconds, the rope will be 47 ft left.

:

:

In 10th cut, total time taken is 10 seconds, the rope will be 40 ft left.

In 11 seconds, the rope will be 39 ft left.

:

:

In 40 seconds, the rope will be 10 ft left.

In 41 seconds, the rope will be 9 ft left.

:

:

In 47 seconds, the will be 3 ft left.

In total time taken of 48 seconds, the rope left will be 2 ft.

Now, in order to cut this 2 ft rope into two 1 ft rope only 1 second will be required, because the rope left will itself be equal to 1 ft.

$\therefore$ Total time taken to cut this 50 ft rope = 48 + 1 = 49 seconds.

So, the answer is 49 seconds.

Answer 2

Given :

We have to cut 50 ft long rope into 1 foot pieces. It takes 1 second to cut it into a one-foot piect.

To Find :

How long would it take to cut the entire rope into one-foot pieces.

Explanation :

The length of the rope = 50 feet.

To cut it into one-foot pieces we have to make number of cuts = 49 cuts

You can see the picture of 10 feet rope dividing into 10 parts by 9 cuts attached alongwith.

∵ Making one cut takes time = 1 second

∴ To cut 49 cuts takes time = 49 seconds

It will take 49 seconds to cut the entire rope into one-foot pieces.