How long does it take to fill up the tank?

Question

It's a really simple question yet I cannot come up with the answer for it,

we have a tank of water, and we have $4$ people if they try to fill the tank separately it will take

$1$st person $60$ minutes to fill
$2$nd person $45$ minutes to fill
$3$rd person $30$ minutes to fill
$4$th person $15$ minutes to fill

how long does it take to fill the tank if they simultaneously try to fill the tank?

I've already tried to divide the first 3 persons time by the 4th persons time and get the final time

so if the 1st person and the 4th person try to fill the tank up

$15 / 4$(since it takes the first person 4 times as the last one). we get $3.75$ and subtract the total time it will be $11.25$

$15 / 3 = 5$ final time would be $11.25 - 5 = 6.25$

$15 / 2 = 7.5$ final time would be $6.25 - 7.5 = -1.25$

doing this will give me a negative result which is why I think my approach in incorrect

Welcome to MSE. Here's how to ask a good question. Follow these guidelines to get help in this forum. It's particularly important that you share your own work and thoughts on the problem to show that you have made a serious effort by yourself before asking for help, and you're not just trying to get others to solve it for you. This is not a homework service. — jjagmath, Dec 11 '22 at 09:34
@jjagmath thanks i've made an edit and specified what i've tried to do already — Sarkar, Dec 11 '22 at 09:40

score 7 · Accepted Answer · answered Dec 11 '22 at 09:48

7

Hint: the first person fills $\tfrac{1}{60}$ per minute, the second fills $\tfrac{1}{45}$ per minute, together they will fill $\tfrac{1}{60}+\tfrac{1}{45}$ per minute.

answered Dec 11 '22 at 09:48

jjagmath

18,214

1

so $1/60 + 1/45 + 1/30 + 1/15 = 0.138888889$? – Sarkar Dec 11 '22 at 09:59
4

The sum in your comment is correct, but you still need to understand what that number means to get to the answer. – jjagmath Dec 11 '22 at 10:03
I can't really figure it out – Sarkar Dec 11 '22 at 10:31
1

@Sarkar What unit do those numbers have? What unit should your final answer have? – Arthur Dec 11 '22 at 10:32
4

it takes 0.1388 per minute so it should get filled up in $7.2$ minutes – Sarkar Dec 11 '22 at 10:57
1

Yes, that's the answer. – jjagmath Dec 11 '22 at 11:01

Sarkar · Answer 2 · 2022-12-11T18:14:05.707

3

Thanks to @jjagmath and @Arthur

the first person fills up $1/60$ per minute

the second person fills up $1/45$ per minute

the third person fills up $1/30$ per minute

the fourth person fills up $1/15$ per minute

sum of all the fractions will be $0.138888889$

that's mean they fill $0.138888889$ per minute and in order to the tank to get filled it would take $1/0.138888889 = 7.2$ minutes

edited Dec 11 '22 at 18:14

answered Dec 11 '22 at 11:08

Sarkar

181

2

If you find my hint useful you could accept my answer. – jjagmath Dec 11 '22 at 12:04
1

We usually work with minutes and decimal seconds, rarely in decimal minutes. So better use rational calculation $\frac{36}{5}=7+\frac 15$ and convert the $\frac 15$ to $12$ seconds. – zwim Dec 11 '22 at 12:30

How long does it take to fill up the tank?

2 Answers2