See my previous post for background. Note that I did edit that post on 6/21.

The question is:

The collegiate training center is currently undergoing renovations and all 6 teams of 124 athletes need to share a smaller facility. You modify the facility arrangement to fit slightly more power racks – for a total of 7. The athletic director insists on every athlete maintaining their 1 hour of strength training. The training center is open 8 hours, but every athlete is pairing up and sharing racks operating at a 1:1 work:rest ratio. However, since you are using power racks assume that racking and re-racking weights will cause a 15% drop in efficiency in rack use. The athletic director asks if you figured out a plan for the athletes, what do you tell him? I. We**can’t**accommodate the athletes

II. We

**can**accommodate the athletes

III. We need the facility open 1 more hour

IV. We need the facility open 4 more hours A. II only

B. I only

C. II and III

D. II and IV

In questions like these, I like to think of it in terms of needs and resources

## Needs

By needs I simply mean how many resources are required to get the task done. We have 6 teams and 124 athletes, but in this case we aren’t given any scheduling or segregation requirements between the teams – **so the number 6 is irrelevant**. Each athlete requires 1 hour of strength training, but will be pairing up and operating at 1:1 work:rest ratio. So in terms of time at the station they will only really need 30 minutes. However due to the 15% loss in efficiency due to racking and re-racking weights, each athlete will need closer to 35minutes. Multiply this number by 124 athletes and you get the total number of rack-minutes you need.

## Resources

The training center is open 8 hours, with 7 racks.

8 hours x 60min/1hour x 7 racks = 3360 rack-minutes. Notice again I like to keep descriptive “made up” units to describe the resources available. Rack-minutes are a resource just like any material resource that we use math to describe (8 six packs x 6beers/six pack = 48 beers, etc).

A quick comparison of our needs vs resources reveals 4340 – 3360 = 980 that we are still in need of 980 minutes of platform-minutes. If we look at the possible answers to the question, we can go back and calculate which option yields us the best answer.

1 additional hour gets us 1 hour x 60min x 7 stations = 420 minutes

4 additional hours gets us another 1680 minutes

See from the math that we really only need 980 extra minutes, somewhere between 2 and 3 hours. However since 3 hours isn’t an option, the correct answer is the one that BEST meets the objectives in question – 1 hour isn’t enough, and even though 4 hours is overkill – it’s the only answer that meets our needs. So the answer is D.

We **can**** **accommodate the athletes **and
**We need the facility open an additional four hours

Can you explain me the 1:1 work:rest = 30 min ?