Your friend is working as a camp counselor, and he is in charge of organizing ac

Question

Your friend is working as a camp counselor, and he is in charge of
organizing activities for a set of junior-high-school-age campers. One of
his plans is the following mini-triathalon exercise: each contestant must
swim 20 laps of a pool, then bike 10 miles, then run 3 miles. The plan is
to send the contestants out in a staggered fashion, via the following rule:
the contestants must use the pool one at a time. In other words, first one
contestant swims the 20 laps, gets out, and starts biking. As soon as this
first person is out of the pool, a second contestant begins swimming the
20 laps; as soon as he or she is out and starts biking, a third contestant
begins swimming . . . and so on.)
Each contestant has a projected swimming time (the expected time it
will take him or her to complete the 20 laps), a projected biking time (the
expected time it will take him or her to complete the 10 miles of bicycling),
and a projected running time (the time it will take him or her to complete
the 3 miles of running). Your friend wants to decide on a schedule for the
triathalon: an order in which to sequence the starts of the contestants.
Let’s say that the completion time of a schedule is the earliest time at
which all contestants will be finished with all three legs of the triathalon,
assuming they each spend exactly their projected swimming, biking, and
running times on the three parts. (Again, note that participants can bike
and run simultaneously, but at most one person can be in the pool at
any time.) What’s the best order for sending people out, if one wants the
whole competition to be over as early as possible? More precisely, give
an efficient algorithm that produces a schedule whose completion time
is as small as possible.

Explanation / Answer

First, the basic concept. The main restriction is 1 swimmer at a time, after that you can have multiple runners or bikers. SO, you want the slowest swimmer first, second slowest swimmer 2nd, nth slowest swimmer nth. This lets the slowest go, and then allows others to catch up time during the other events. If somebody had a time in another event that was hugely slower you may want them to go first even if they had a faster swim time, but that biking or running time would appear to be an outlier, and is not present here.Since some have the same swim time you put the contestant w/ the slower second event (bike) first--1&6, and 3&7 have the same swim times.

So, the order they start is: 2,5,1,6,4,7,3

You do the slowest (#2) first, then the second contestant (#5) starts when (#2) is done, which is after 19 minutes (#2's time to swim). Add #2's swim time to #5's (second to start swimming) time to get the time until contestant 3 (#1 in list) starts. Do this for all 7 contestants. This will tell you at what time point each contestant stops swimming. So, if you do this you will find that the last contestant (#7) is done swimming at 99 minutes.

After this you just total each contestant's total swim, bike and run time, and add it to the time they started. So, for the first contestant to go (#2) it is 19+17+13=49 minutes. For the second contestant (#5) it is their start time plus swim time plus other times; 37+13+14=64. For all of them it is;
Contestant, swim, bike, run, total
2 19 17 13 49
5 37 13 14 64
1 52 13 15 80
6 67 10 14 91
4 79 18 17 114
7 89 13 10 112
3 99 13 10 122

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.