Question

A. The number of people working on a certain job varies inversely as the number of days needed to finsih the job. If it takes 10 carpenters to finish a house in 8 days, in how many days will 4 carpenters finish it?

B. The length of a rectangle with a constant area varies inversely as its width. The length of this rectangle is 8in when its width is 3 inches. Find the length when the width is 4 inches.

Answer 1

1. common sense solution:
if it takes 10 carpenters to do a house in 8 days, then 1 carpenter would take 80 days, and 4 carpenters would take 20 days.

2. by the "constant" method
number of days = k/number of carpenters
given:
8 = k/10
k = 80

so number of days = 80/number of capenters
so for 4 carpenters,
number of days = 80/4 = 20

3. the inverse proportion way:
n1 of carpenters/n2 of carpenters = days2/days1
10/4 = days2/8
days2 = 8(10)/4 = 20

notice the actual arithmetic or calculation is the same for all 3 methods.

Pick one of the above ways to do the 2nd question.