Question

will the pool be full?
read the situation below and answer the questions that follow.
suppose you are a tasked to organize a pool party for your best friends birthday your other friends suggested that it has to be held in the lone inland resort in the city you decided not to book the event in advance and planned to just come to the resort early to arrange for the pool party on that same day however when you came to the resort you had been informed that the pool was drained and his schedule to be refilled within the day one pipe can feel the empty pool in 12 hours and another can fill the empty pool in 18 hours suppose both pipes are opened at 8:00 a.m. and you have schedule the pool party for your best friends birthday at 2:00 pm on the same day.
Question:
1. will the pool be filled by 2:00 pm? elaborate your answer
2. at what exact time will the pool be completely filled?
3.would the situation be different if you have booked for the event ahead of time?
4. what do you think should be the best decision make?
A. cancel the event
B. movie schedule at a later time within a day
C. move the schedule at an earlier time within the day. ​

Answer 1

Given :

Its given that the first pipe can fill the pool in 12 hours. and the second pipe can fill the pool in 18 hours.

To Find :

We have to find that if both the pipes are been opened then in how much time the pool will been filled.

Solution :

Since they said if the pipe been opened while 8 AM will it filled by 2 pm. So the pipes should fill the pool in 6 hours.

Let's have the time by which both the pipes fill the pool as x.

It's given that ,

First pipe can fill the pool = 12 hours

then the water filled in the pool in 1 hour =

$\frac{x}{12}$

Second pipe can fill the pool = 18 hours.

then the water filled in the pool in 1 hour =

$\frac{x}{18}$

The Time taken by both the pipes to fill the pool =

$\frac{x}{12} + \frac{x}{18} = 1 \\ \frac{18x + 12x}{216} = 1 \\ \frac{30x}{216} = 1 \\ 30x = 216 \\ x = \frac{216}{30} \\ x = 7.2 \: hours$

The time taken by both the pipes to fill the pool is 7 hours and 20 mins.

1. No the pool cant be filled by 2pm because the time taken by 2 pipes is exactly 7 hours and 20 mins. As by given the pool should be filled in 6 hours.

2. The pool will be filled Exactly at 3:20 AM

3.yes the situation will be different when we booked the event ahead of time.

4. Move schedule at the later time within the day

Answer 2

Given :

Its given that the first pipe can fill the pool in 12 hours. and the second pipe can fill the pool in 18 hours.

To Find :

We have to find that if both the pipes are been opened then in how much time the pool will been filled.

Solution :

Since they said if the pipe been opened while 8 AM will it filled by 2 pm. So the pipes should fill the pool in 6 hours.

Let's have the time by which both the pipes fill the pool as x.

It's given that ,

First pipe can fill the pool = 12 hours

then the water filled in the pool in 1 hour =

$\frac{x}{12}$

Second pipe can fill the pool = 18 hours.

then the water filled in the pool in 1 hour =

$\frac{x}{18}$

The Time taken by both the pipes to fill the pool =

$\frac{x}{12} + \frac{x}{18} = 1 \\ \frac{18x + 12x}{216} = 1 \\ \frac{30x}{216} = 1 \\ 30x = 216 \\ x = \frac{216}{30} \\ x = 7.2 \: hours$

The time taken by both the pipes to fill the pool is 7 hours and 20 mins.