If it takes 15 people 8 hours to make 100 items, howmany hours will it take six people ...?

Question

Please help me solve it,
If it takes 15 people 8 hours to make 100 items, howmany hours will it take six people working at the same rate, to make half as many items?

Answer 1

10 hours

100 items / 8 hours = 12.5 items/hour
12.5 / 15 people = .833333 items per person per hour
.8333 * 6 people = 5 items per hour
50 total items needed / 5 items per hour = 10 hours

Answer 2

The # of people varies inversely with the time (as one quantity increases, the other decreases). The number of items made varies directly with the time (i.e., proportional). So you can set up a little proportion:

(15*8)/100 = (6*T)/50

T = 10 hours

Answer 3

15 people-----100 items-----8 hours
6 people-------50 items------15/6 x 1/2 x 8 hours
------------------------------- = 10 hours