How long will it take to fill the pool?

Three water pipes are used to fill a swimming pool. The first pipe alone takes 8 hours to fill the pool, the second pipe alone takes 12 hours to fill the pool, and the third pipe alone takes 24 hours to fill the pool. If all three pipes are opened at the same time, how long will it take to fill the pool?

MetroEye: This problem is similar to work-time problem. Refer MetroEye02

As per the formula,
\(\dfrac{1}{t} = \dfrac{1}{8} + \dfrac{1}{12}+ \dfrac{1}{24}= \dfrac{3 + 2 + 1}{24}  =  \dfrac{6}{24} =  \dfrac{1}{4}\)

=> t = 4

It will take 4 hours to fill the pool if all three pipes are opened at the same time.

How long will the supplies then last?

Twelve people purchased supplies for a ten-day camping trip with the understanding that each of the twelve will get equal daily shares. They are then joined by three more people, but make no further purchases. How long will the supplies then last if the original daily share for each person is not changed?

MetroEye: Rate of Work

Here \(M_1\) = 12
\(H_1\) = 10 days
Let supplies = S

When 3 more people joined, \(M_2\) = 12+3 = 15

As per the MetroEye, \(\dfrac{S}{12\cdot 10}\) = \(\dfrac{S}{15\cdot H_2}\)
=\(\dfrac{120}{15}\) = 8

The original supplies will last only for 8 days.

How much time would it take for Amy to mow 600 square feet?

Amy can mow 600 square yards of grass in \(1 \dfrac{1}{2}\) hours. At this rate, how many minutes would it take her to mow 600 square feet?

MetroEye: Rate of Work

1 square yard = 1 square feet
\(1 \dfrac{1}{2}\) hours = \(\dfrac{3}{2}\cdot 60\) = 90 minutes

\(\dfrac{600 sq yards}{1 \cdot 1 1/2 hours}\) = \(\dfrac{600 sq feet}{1 \cdot H_2}\) 

Converting to same units,

\(\dfrac{600\cdot 9}{90}\) = \(\dfrac{600}{H_2}\) 

\(H_2\) = \(\dfrac{600\cdot 90}{600\cdot 9}\) = 10 minutes

Amy would take 10 minutes to mow 600 sq.feet.

How long it would take to complete the work at the same rate?

A work crew of 3 people requires 3 weeks and 2 days to do a certain job. How long would it take a work crew of 4 people to do the same job if each person of both crews works at the same rate as each of the others? Note : each week contains six work days.

MetroEye: This problem is  the work-person-rate problem.
i.e; W₁/(M₁×H₁) = W₂/(M₂×H₂)
where W is work to be done,  M is the number of persons required, Hour is time required. 

Here as the work done is same W₁ = W₂
=> M₁×H_{1 =} M₂×H₂
H₁= 3 weeks 2 days = 3×6+2=20 days
=> 3×20= 4 × H₂
H₂ = 60÷4 = 15 days = 2 weeks 3 days
So 4 people should work 2 weeks and 3 days to do the same job.

Chicken-Egg-Days Problem

7 Chicken lays 8 eggs in 64 days. If we need 27 eggs in 42 days how many chickens we need?

MetroEye: This problem is similar to work-person-rate problem.

i.e; W1/(M1*H1) = W2/(M2*H2)
where W is work to be done,  M is the number of persons required, Hour is time required. 

Applying the above equation 
8/(7*64) = N/(27*42) where N is the number of chickens needed.

Solving N = 36

36 Chickens are needed to get 27 eggs in 42 days.