[MOVED] problem solving: when will mouse reach top?

[math78]

A mouse is at the bottom of a 10 foot tall clock. Every hour he climbs up 3 feet. But when the clock strikes at the hour, he falls back 1 foot. If the mouse starts climbing at 8am, at what time to the nearest minute will it reach to the top of the clock?

 

[stapel]

In the first hour, to what height does he climb? On the hour, how far back does he fall? So what is his ending height, after the first hour?

After hour many hours will he be three feet from the top?

At the end of one more hour, just before the clock strikes, at what height will he be?

:wink:

Eliz.

 

[Denis]

A mouse is at the bottom of a 10 foot tall clock.

Are you sure it's not an 11 foot tall clock?
10 feet takes the "fun" out of it !

 

[Deleted member 4993]

Or 9' tall pole - or sliding back 2'....

 

[soroban]

Hello, math78!

A mouse is at the bottom of a 10-foot tall clock.
Every hour he climbs up 3 feet, but when the clock strikes at the hour, he falls back 1 foot.
If the mouse starts climbing at 8am, at what time, to the nearest minute,
will it reach to the top of the clock?

This is a classic "trick question".


Incorrect solution

Since it climbs three feet and falls one foot each hour, it progresses two feet per hour.
To climb ten feet, it must take five hours.
. . Therefore, it reaches the top at 1:00 p.m. . Wrong!


Correct solution

It is true that it climbs two feet per hour.
At the end of four hours (12 noon), it has climbed eight feet.
During the next hour, it climbs the remaining two feet and stops.
The two-foot climb takes 2/3 of an hour (40 minutes).
. . Therefore, it reaches the top at \(\displaystyle \fbox{12:40\text{ p.m.}}\)