Question

@mathmale Could you help me?

On Mondays, Tuesdays, and Wednesdays, Peter does between 3 and 6 hours of homework per night. On the other four days of the week, Peter does between 1 and 4 hours of homework per night. What is a reasonable amount of time that Peter spends doing his homework each week?

10 hours
37 hours
23 hours
41 hours

Answer 1

How many nights of the week does Peter do between 3 and 6 hours of homework each night?

Answer 2

3

Answer 3

wait 4

Answer 4

Right. If that's the case, what's the minimum number of hours he'd study, total, if we focus only on those three nights? the max?

Answer 5

umm... 23?

Answer 6

wait 10 not 23

Answer 7

I'm breaking this problem down into parts, so am asking you questions whose answers we'll put together into a whole later.

3 nights per week, 3 hours per night, comes to how many hours?
3 nights per week, 6 hours per night, comes to how many hours?

Answer 8

first one 9

second one 18

Answer 9

Right. So, on Mondays, Tuesdays and Wednesdays, this student studies between 9 and 18 hours per week. Would you disagree or agree with that?

Answer 10

agree

Answer 11

"On the other four days of the week, Peter does between 1 and 4 hours of homework per night." What range of hours would he study each week on these four days?

Answer 12

between 1 and 4

Answer 13

For the day or for the week?

Answer 14

umm days

Answer 15

It's too early to "agree" or "disagree" here.

Answer 16

And so, for the week, the range of hours Peter studies for those four days is what?

Answer 17

Is that all? Remember, we're talking about four days and a range of 1 to 4 hours per day.

Answer 18

wait no... i'm confused

Answer 19

9

Answer 20

Please write a range of hours, as you did last time. Four days per week minimum 1 hour per day, up to 4 hours per day, gives us what range of hours?

Answer 21

9 and 18 if not then im confused

Answer 22

Four days per week, 1 hour per day, comes to 4 hours.
Four days per week, 4 hours per day, comes to ...

Answer 23

wait i think i got it

(3 × 4.5) + (4 × 2.5) = 23 hours

Answer 24

For these four days, the range is from 4 hours (the minimum) to ( ? ) hours (the maximum).

Answer 25

If Peter averages 4.5 hours of homework on Monday through Wednesday, and 2.5 hours the other days, the total hours of homework can be calculated by the following:

(3 × 4.5) + (4 × 2.5) = 23 hours

Answer 26

As before: I have broken this problem down into parts and have been asking you to address each part separately. I think you're trying to look at the problem as a whole right off, right now.

What I've pointed out so far is that on Mondays, Tuesdays and Wednesdays, Peter studies from 9 to 18 hours. Go back and check that for yourself; you wrote it that way.

On the other four nights, Peter studies betwwen 1 and 4 hours per night, or between (how many?) hours and (how many?) hours on Thurs, Fri, Sat and Sun.

Answer 27

well i input 23 as my answser and that's how i figured it out and it came out right.

Answer 28

Hints: 4*1=4, and 4*4=16.

All right. Glad you have the correct answer. As you can probably guess, my aim is always more that you, my student, understand the process of solving the problem in question than it is getting the right answer.

Answer 29

I understand that completley :) Thank you :)

Answer 30

You are always free to attack a given problem in your own way, as you've done here. I'd thought it might make the problem solving easier for you if we were to break it down into simpler parts, but apparently that proved to be more confusing than helpful.

glad you are satisfied. Good luck!