Question

In each 24-hour period, I sleep for twice as long as I play. I work for twice as long as I eat. I do nothing for half as long as I work. I play for two-thirds as long as I work. How many hours do I sleep, eat, play, work, and do nothing?

A. Sleep: 8, Eat: 2, Play: 6, Work: 12, Do nothing: 3
B. Sleep: 6, Eat: 3, Play: 4, Work: 8, Do nothing: 2
C. Sleep: 4, Eat: 1, Play: 2, Work: 4, Do nothing: 1
D. Sleep: 10, Eat: 5, Play: 8, Work: 16, Do nothing: 4

Answer 1

In each 24-hour period, I sleep for twice as long as I play. I work for twice as long as I eat. I do nothing for half as long as I work. I play for two-thirds as long as I work. Therefore,the correct Option is Option A. Sleep: 8, Eat: 2, Play: 6, Work: 12, Do nothing: 3

Step-by-step explanation:

To find the solution, let's represent each activity with a variable: S for sleep, E for eat, P for play, W for work, and D for do nothing. The given information can be translated into equations:

1. (S = 2P)

2. (W = 2E)

3. (D = 0.5W)

4.
`\(P = (2)/(3)W\)`

Now, let's express everything in terms of a single variable. Using equation (1), we can express sleep in terms of play: (S = 2P). Substituting this into equation (4) gives
`\(P = (2)/(3)(2P)\)` . Solving for P, we get (P = 3).

Now, substitute this value of P into equations (2), (3), and (4) to find the values of other variables:

2. (W = 2E): (W = 2(3) = 6

3. (D = 0.5W): (D = 0.5(6) = 3

4.
`\(P = (2)/(3)W\): \(P = (2)/(3)(6) = 4\)`

5. (S = 2P): (S = 2(4) = 8)

So, the correct answer is A. Sleep: 8, Eat: 2, Play: 6, Work: 12, Do nothing: 3