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16 Dec 2025, 19:37
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Minimum: 17.5
Maximum: 19.5
We want to find the minimum and maximum amount of time it will take for these four people to complete the task in a four-person cycle. As the project manager, we can assume we can order them however we want.
Therefore, to minimize the time, place the faster people first, and to maximize, place the slower people first.
First rewrite the amount of units of work each can complete in terms of 80 which is the LCM of all numbers.
A - 10/80, B - 4/80, C - 2/80, and D 1/80.
If we order them A -> B -> C -> D, 10+4+2+1 = 17 units of work completed in one four-hour cycle. Let's figure out how many four hour cycles we need to complete 80 units of work, 80/17 = 4 and 12/17. Therefore, 4*4=16 hours, plus the work of A and half the work of B to reach 12 hours, which is 1.5. So minimum time = 17.5 hours.
Maximum time would be:
Order them D -> C -> B -> A
We know this cycle will complete the same amount of work at 17 units, but this time in order to reach the 12 extra hours, we are going from 1 -> 2 -> 4 -> 10. So we need to go use D, C, B, and half of A's work - which is 16 + 3.5 hours or 19.5 hours. Therefore, 19.5
This took me a while to do, does anyone have a faster way to get this under two minutes?
Maximum: 19.5
We want to find the minimum and maximum amount of time it will take for these four people to complete the task in a four-person cycle. As the project manager, we can assume we can order them however we want.
Therefore, to minimize the time, place the faster people first, and to maximize, place the slower people first.
First rewrite the amount of units of work each can complete in terms of 80 which is the LCM of all numbers.
A - 10/80, B - 4/80, C - 2/80, and D 1/80.
If we order them A -> B -> C -> D, 10+4+2+1 = 17 units of work completed in one four-hour cycle. Let's figure out how many four hour cycles we need to complete 80 units of work, 80/17 = 4 and 12/17. Therefore, 4*4=16 hours, plus the work of A and half the work of B to reach 12 hours, which is 1.5. So minimum time = 17.5 hours.
Maximum time would be:
Order them D -> C -> B -> A
We know this cycle will complete the same amount of work at 17 units, but this time in order to reach the 12 extra hours, we are going from 1 -> 2 -> 4 -> 10. So we need to go use D, C, B, and half of A's work - which is 16 + 3.5 hours or 19.5 hours. Therefore, 19.5
This took me a while to do, does anyone have a faster way to get this under two minutes?
16 Dec 2025, 19:57
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Suppose that total work is 80.
Alex can complete 80/8 = 10 in 1 hour
Beth can complete 80/20 = 4 in 1 hour
Charles can complete 80/40 = 2 in 1 hour
Dana can complete 80/80 = 1 in 1 hour
After the first cycle they have completed 10+4+2+1=17
After the second cycle they have completed 17+17=34
After the third cycle they have completed 34+17=51
After the fourth cycle they have completed 51+17=68
80-68=12 -> no need of another complete cycle.
To minimize the number of hours people with higher rate should work first. Alex add 10 in 1 hour and Beth add 2 in half an hour to complete the task.
To maximize the number of hours people with lower rate should work first. Dana add 1 in 1 hour, Charles add 2 in 1 hour, Beth add 4 in 1 hour and Alex add 5 in half an hour to complete the task.
4 cycles = 4*4=16 hours
minimum=16+1.5=17.5
maximum=16+3.5=19.5
Alex can complete 80/8 = 10 in 1 hour
Beth can complete 80/20 = 4 in 1 hour
Charles can complete 80/40 = 2 in 1 hour
Dana can complete 80/80 = 1 in 1 hour
After the first cycle they have completed 10+4+2+1=17
After the second cycle they have completed 17+17=34
After the third cycle they have completed 34+17=51
After the fourth cycle they have completed 51+17=68
80-68=12 -> no need of another complete cycle.
To minimize the number of hours people with higher rate should work first. Alex add 10 in 1 hour and Beth add 2 in half an hour to complete the task.
To maximize the number of hours people with lower rate should work first. Dana add 1 in 1 hour, Charles add 2 in 1 hour, Beth add 4 in 1 hour and Alex add 5 in half an hour to complete the task.
4 cycles = 4*4=16 hours
minimum=16+1.5=17.5
maximum=16+3.5=19.5
16 Dec 2025, 20:22
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Alex, Beth, Charles and Dana rates are 1/8, 1/20, 1/40 and 1/80 respectively. Or 10/80, 4/80, 2/80 and 1/80 using the common 80 as denominator.
In each cycle the complete 10/80 + 4/80 + 2/80 + 1/80 = 17/80 of the task.
In 4 cycles (16 hours) they complete 4*17/80 = 68/80 of the task.
12/80 of the task still need to be completed.
Minimum if the order in the cycle is Alex(highest rate), Beth(second highest rate), Charles(third highest rate) and Dana(fourth highest rate)
Alex add 10/80 in 1 hour -> still needed 2/80
Beth add 2/80 in 0.5 hours
Using 1.5 hours for a total of 17.5 hours
Maximum if the order in the cycle is Dana(lowest rate), Charles(second lowest rate), Beth(third lowest rate) and Alex(fourth lowest rate)
Dana add 1/80 in 1 hour -> still needed 11/80
Charles add 2/80 in 1 hour -> still needed 9/80
Beth add 4/80 in 1 hour -> still needed 5/80
Alex add 5/80 in 0.5 hours
Using 3.5 hours for a total of 19.5 hours
Minimun is 17.7 and Maximum is 19.5
In each cycle the complete 10/80 + 4/80 + 2/80 + 1/80 = 17/80 of the task.
In 4 cycles (16 hours) they complete 4*17/80 = 68/80 of the task.
12/80 of the task still need to be completed.
Minimum if the order in the cycle is Alex(highest rate), Beth(second highest rate), Charles(third highest rate) and Dana(fourth highest rate)
Alex add 10/80 in 1 hour -> still needed 2/80
Beth add 2/80 in 0.5 hours
Using 1.5 hours for a total of 17.5 hours
Maximum if the order in the cycle is Dana(lowest rate), Charles(second lowest rate), Beth(third lowest rate) and Alex(fourth lowest rate)
Dana add 1/80 in 1 hour -> still needed 11/80
Charles add 2/80 in 1 hour -> still needed 9/80
Beth add 4/80 in 1 hour -> still needed 5/80
Alex add 5/80 in 0.5 hours
Using 3.5 hours for a total of 19.5 hours
Minimun is 17.7 and Maximum is 19.5
