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

Answer:

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

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:

$1\ inch=\frac{1}{12}\ feet\\ \therefore 48\ inches\ =\ 48\ \times \frac{1}{12}\\ =\frac{48}{12}\\ = 2 feet$

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