Question

The depth of water at the end of a pier varies with the tides. The low tides occur on a particular day at 2:00 a.m. and 2:00 p.m. with a depth of 1.1 m. The high tides occur at 8:00 a.m. and 8:00 p.m. with a depth of 5.3 m. A large boat needs at least 3 m of water to be safely secured at the end of the pier. What is the first time in the morning that is it safe for the boat to be tied to the pier

Answer 1

4:42 a.m.

Explanation:

The earliest low tide occurs by 2:00 a.m. and the earliest high tide occurs by 8:00 a.m.

Between these hours, 6 hours elapsed.

The lowest point is 1.1 m and increases steadily to 5.3 m.

Let us take 2:00 a.m. as the zeroth hour, and 8:00 a.m. as the 6th hour, we can safely interpolate as below,

0 = 1.1 m

x = 3 m

6 = 5.3 m

we solve as
`(x - 0)/(6 - 0)` =
`(3 - 1.1)/(5.3 - 1.1)`

`(x)/(6)` =
`(1.9)/(4.2)`

4.2x = 11.4

x = 2.71 hours from 2:00 a.m.

= 2 hrs + (0.71 x 60)min = 2 hrs 42.6 min

the time will approximately be by 4:42 a.m.