SOLUTION: Hi A team of 15 fruit pickers can clear 6 hectares in a week. How many days would it take 21 fruit pickers. If 6 hectares had to be cleared in 2 days how many pickers would be

Question 1183745: Hi
A team of 15 fruit pickers can clear 6 hectares in a week.
How many days would it take 21 fruit pickers.
If 6 hectares had to be cleared in 2 days how many pickers would be needed.
Thanks
Found 3 solutions by Theo, greenestamps, josgarithmetic:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the formula that i use for problems such as this is:
p * r * t = q
p is the number of people.
r is the average rate that each person works.
t is the time.
q is the quantity.

the implicit assumption is that each person always works at the average rate per person.
that is assumed to be a constant.

in your problem, p * r * t = q becomes:
15 * r * 7 = 6
solve for r to get:
r = 6 / (15 * 7) = 6/105 = .057428571, which i stored in a variable called x.
the formula then becomes:
p * x * t = q
when p = 15 and t = 7, the formula becomes:
15 * x * 7 = q
solve for q to get:
q = 15 * x * 7 = 6.

this confirms the average rate per person is accurate.

when p = 21, the formula becomes:
21 * x * t = 6
solve for t to get:
t = 6 / (21 * x) = 5.

with 15 people working, it takes 7 days.
with 21 people working, it takes 5 days.

if the same quantity has to be done in 2 days, the formula becomes:
p * x * 2 = 6
solve for p to get:
p = 6 / (2 * x) = 52.5 days.

don't forget, .....
x = 6/105 = .0571428571.
that's the average rate per person that is assumed to be a constant.

in real life, it probably is not.

Answer by greenestamps(13216)   (Show Source): You can put this solution on YOUR website!

The other tutor provides a response showing a formal mathematical method for solving the problem, using a formula relating the quantity to the number of workers, the rate of the workers, and the amount of time. That approach is fine; and it is useful if you are going to need to work problems with a large number of different sets of input data.

For solving a problem like this, with one set of given data and just two specific alternate sets of data, I find an informal solution is much faster and easier.

Given: 15 fruit pickers, one week (7 days), 6 hectares.

First question: 21 fruit pickers instead of 15 (and, presumably, since not stated otherwise, the same 6 hectares).

Solution: 21/15 = 7/5 as many workers means 5/7 as many days: (5/7)*7 = 5

ANSWER: 5 days with 21 workers

Second question: 2 days instead of 7 days, and the same 6 hectares.

Solution: 2/7 as many days means 7/2 as many workers: (7/2)*15 = 105/2 = 52.5

ANSWER: 53, if a whole number is required; or 52.5, if one worker can work half a day.

Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!
15 pickers
6 hectares
1 week

Assuming 7 days for 1 week, then for some constant picker rate r,
.

How many days of time for 21 fruit pickers (the same number of 6 hectares?)?
x, number of days,
.

Both left-side members are equal to 6.

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