Question

If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

Answer 1

It will take `2.73` minutes for all the `3` of them working together to mix the `20` drinks.

Explanation:

As Steven can mix `20` drinks in `5` minutes,

he can mix `20/5=4` drinks in `1` minute.

As Sue can mix `20` drinks in `10` minutes,

she can mix `20/10=2` drinks in `1` minute.

and as Jack can mix `20` drinks in `15` minutes,

he can mix `20/15=4/3` drinks in `1` minute.

Hence, together all `3` can mix `4+2+4/3=22/3` drinks in `1` minute

i.e. `1` drink in `3/22` minutes

and `20` drinks in `20xx3/22=60/22=2.73` minutes.

Answer 2

`2.bar(72)` minutes or `3` minutes for a whole number of drinks.

Explanation:

The least common multiple of `5`, `10` and `15` is `30`. So let's look at how many drinks the team could mix in `30` minutes:

Steven: `20*30/5 = 120`

Sue: `20*30/10 = 60`

Jack: `20*30/15 = 40`

So a total of `120+60+40 = 220` drinks.

So to mix `20` drinks would take the team:

`30*20/220 = 30/11 = 2.bar(72)` minutes.

If each was working on their own, then at the end of `2.bar(72)` minutes they would each be part way through making a drink.

Let us see how far they would get:

Steven: `120/11 = 10 10/11`

Sue: `60/11 = 5 5/11`

Jack: `40/11 = 3 7/11`

So that's `18` whole drinks. So we would require two of the team to finish to get the whole `20` drinks, or one of the team to finish one and make a complete extra one.

Let us see how much more time they need to complete the partial drink:

Steven: `1/11*5/20 = 1/44` minutes

Sue: `6/11*10/20 = 3/11` minutes

Jack: `4/11*15/20 = 3/11` minutes

So we would have to wait `3/11` minutes for two more of the team to finish, by which time all three would have finished.

`30/11+3/11 = 33/11 = 3`

So `3` minutes total, by which time Steven could have finished making his `12`th drink, giving a total of `12+6+4 = 22` drinks.

If it is possible to break down the stages of preparation of a drink in order that more than one person can work on it, then it may be possible to achieve the `20` whole drinks in `2.bar(72)` minutes.

For example:

• Jack completes `1/11`th of a drink before handing it to Steven to complete. (Steven may finish making `10` whole drinks before he gets around to it)
• Jack completes `6/11`ths of a second drink before handing it to Sue to complete. (Sue may finish making `5` whole drinks before she gets around to it)
• Jack completes `3` whole drinks in the remaining time.