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1.A tennis pro's workout schedule is to have both morning and afternoon practice for 3 days, rest for 1 day, have only morning practice for 2 days, rest for 2 days, and then start the cycle again. If thetennis pro is on her rest for one day part of the schedule, determine what she will be doing a) 20 days from today, b) 47 days from today, c) 106 days from today, and d) Will the tennis pro have a dayoff 76 days from today?

Sagot :

1) We have the schedule of the tennis player.

First, we have to identify the period of the cycle. That is how many days it takes to start over.

We have this schedule:

1) both morning and afternoon practice for 3 days,

2) rest for 1 day,

3) have only morning practice for 2 days,

4) rest for 2 days

If we take each We have 3+1+2+2 = 8 days.

Then, for example each day will be equal to 8 days before or 16 days before for example.

This can be generalized as 8n, where n is an integer.

Then, as we have to idenfity the reference day.

It says that it is now in the 1-day rest period (after the 3 days of both morning and afternoon practice), so that is our reference point.

a) We have to find what he will be doing 20 days from today.

As the cycle is 8 days, we will have completed 2 cycles, totaling 16 days and we are left with 20-16 = 4 days.

Then, we can draw a circle that represents the cycle and check for the position after 4 days:

We jumped 4 times (one per day) from today (after 2 complete cycles) and we land on "rest".

b) We have to find what he will be doing after 47 days.

If we divide 47 by 8 we get 5.875.

This means that 5 cycles have been completed in that period of time.

The remaining days can be calculated as 0.875*8 = 7, so we can find what he will be doing by jumping back one day (NOTE: like doing 6 complete cycles and jumping back in time one day).

We can see in the cycle that he would be training both in the morning and afternoon (3rd day of training).

c) We have to find what he will be doing after 106 days.

Dividing 106 by 8 we get 13 complete cycles and 2 days remaining.

If we jump two times in the cycle from today we get that he would be training in the morning.

As this is the second day of the second phase of training, it correspond to the fifth day of training.

d) We have to find what he will be doing after 76 days.

This corresponds to 9 complete cycles and 4 days from today.

The same that for point (a) we can conclude that he will be resting that day, so he will have a day off.

Answer:

a) Resting

b) Training morning and afternoon (third training day of the cycle, Option C)

c) Training in the morning (fifth training day of the cycle, Option D)

d) Yes.

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