Question

There are two clocks on a wall, both set to show the correct time at 8:00a.M. One clock loses two minutes in an hour while the other gains one minute in one hour. By how many minutes do the two clocks differ at 12 noon on the same day?

Answer 1

Since the wall clock gains 22 minutes every 1212 hours, it really gains t360t360 hours every tt hours (e.g., 12360=13012360=130 and 130130 hours is equivalent to 22 minutes). Thus, we can let the total time elapsed on WcWc for tt hours be

Wc=t+t360.(1)

(1)Wc=t+t360.

For the table clock, TcTc, we actually lose 22 minutes every 3636 hours; that is, we lose t1080t1080 hours every tt hours (for example, 361080=130361080=130 and 130130 hours is equivalent to 22 minutes, as described above). Thus, we can let the total time elapsed on TcTc for tt hours be

Tc=t−t1080.(2)

(2)Tc=t−t1080.

Now what? This depends on the kind of clock you are using. If you are using a regular wall-clock that does not differentiate between AM and PM (i.e., a 12-hour clock), then we will need to figure out when

Wc−Tc=12.(3)

(3)Wc−Tc=12.

However, if you are using a clock that does differentiate between AM and PM, then you will need to figure out when

Wc−Tc=24.(4)

(4)Wc−Tc=24.

Using a 12-hour clock: We substitute (1)(1) and (2)(2) into (3)(3) to get

t360+t1080=12⟺4t=12960⟺t=3240.

t360+t1080=12⟺4t=12960⟺t=3240.

Thus, 32403240 hours will have elapsed. Note that

3240hours=19weeks⋅168hours/week+48hours.

3240⏟hours=19⏟weeks⋅168⏟hours/week+48⏟hours.

Thus, 1919 weeks and 4848 hours will have elapsed. Since your clocks began on a Tuesday at noon, they will next meet again on Thursday at noonThursday at noon.

Using a 24-hour clock: We substitute (1)(1) and (2)(2) into (4)(4) to get

t360+t1080=24⟺4t=25920⟺t=6480.

t360+t1080=24⟺4t=25920⟺t=6480.

Thus, 64806480 hours will have elapsed. Note that

6480hours=38weeks⋅168hours/week+96hours.

6480⏟hours=38⏟weeks⋅168⏟hours/week+96⏟hours.

Thus, 3838 weeks and 9696 hours (four days) will have elapsed. Since your clocks began on a Tuesday at noon, they will next meet again on Saturday at noonSaturday at noon.

hope this helps

mark me as brainliest plz...

:)

Answer 2

Answer:
answer is 12 MINUTES
Step-by-step explanation:
SEE THE ATTACHMENT