Inverse proportion

haftakhan · 2010-07-05 05:58:10

I need a simple way to solve this question.

It takes 3 men to gig 2 identical trenches in 5 hours .If all the men work at the same rate ,how long will it take 5 men to dig 7 of these trenches ?

i have solved it this way through the help of an example in the book.

Solution

First we keep the number of trenches constant

No of men No of trenches No of Hours

3 2 5

1 2 5*3

5 2 (5*3)/5=3

Next we keep the number of men constant

No of men No of trenches No of Hours
5 2 3

5 1 3/2=1.5

5 7 1.5*7=10.5

Therefore 5 men will take 10.5 hours to dig 7 identical trenches.

I want a simpler solution to this.

ZHero · 2010-07-05 06:12:05

Work done = Number of men × Time tanken × Rate of work

Or, W = N × T × R
Here, in the first case, W = 2, N = 3, T = 5 and R = R
→ 2 = 3 × 5 × R
→ R = 2/(3 × 5) ..... (1)

For the second case, W = 7, N = 5, T = ?, R = R
→ 7 = 5 × ? × R
→ R = 7/(5 × ?) ..... (2)

Equate equations (1) and (2) and you'll get the value of "?"!

bobbym · 2010-07-05 06:23:12

Hi haftakhan;

What's wrong with what you did? How can you beat that for simplicity, you only have to multiply and divide?

1 man can dig 2 / 3 of a trench per 5 hours, now divide by 5

1 man can dig 2 / 15 of a trench per hour. now multiply by 5

5 men can dig 10 / 15 of a trench per hour so 5 men can dig 7 trenches in

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