Question

A ship is at anchor. Over its side hangs a rope ladder with rungs a foot apart. The

tide rises at the rate of 8 inches per hour. At the end of 6 hours, how much of the
rope ladder will remain above the water, assuming that 8 feet were above the
water when the tide began to rise?

Answer 1

After 6 hours, 4 feet of the rope ladder will remain above water.

Step-by-step explanation:

To solve this problem, we need to consider the rate at which the tide rises and the amount of time that has passed.

Let's start with the given information. The tide rises at a rate of 8 inches per hour, and at the beginning, 8 feet (or 96 inches) of the rope ladder are above the water.

After 6 hours, the tide would have risen 6 times 8 inches, which is 48 inches. So, the portion of the rope ladder underwater would be 96 inches - 48 inches = 48 inches. Since there are 12 inches in a foot, the remaining portion of the rope ladder above the water would be 48 inches / 12 = 4 feet.

Answer 2

At the end of 6 hours, 6 feet of the ladder remained above water

Step-by-step explanation:

we are given the following:

change in tide = 8 inches per hour

1 hour = 8 inches

∴ 6 hours = 8 × 6 = 48 inches

Now, since the length of the ladder is measured in foot, let us convert the rate of tide rising to foot.

12 inches = 1 foot

dividing both sides by 12:

`1\ inch=(1)/(12)\ feet\\ \therefore 48\ inches\ =\ 48\ * (1)/(12)\\ =(48)/(12)\\ = 2 feet`

Therefore, after 6 hours, the tide rises by 2 feet.

Next, we are told that the rope ladder at the beginning was 8 feet, hence the length remaining above water after 6 hours of the rising of the tide is calculated as follows:

= 8 feet above water

height of tide = 2 feet = amount submerged in water

∴ length above water = (ladder before rising of the tide) - (amount submerged in water)

length above water = 8 - 2 = 6 feet

Therefore at the end of 6 hours, 6 feet of the ladder remained above water