1. ## Algabaric time messaure...

To a bath there are two taps:
one - fill the bath half an hour.
the second - fill the bath third of the hour.
The taps open together.

What the time the bath will be filled about?

2. ## Re: Algabaric time messaure...

Let's convert to minutes. Tap 1 does the job in 30 minutes while tap 2 does it in 20 minutes.

So, together, it will take $\dfrac{30\cdot 20}{30 + 20} = \dfrac{600}{50} = 12$ minutes.

Thanks.

4. ## Re: Algabaric time messaure...

x = time in hours both taps work together

rate 1 = how many baths tap 1 fills in one hour

rate 2 = how many baths tap 2 fills in one hour

1 = the whole job

x(rate 1 + rate 2) = 1

x(2 + 3) = 1

5x = 1

x = 1/5

1/5 hour

or

12 minutes

5. ## Re: Algabaric time messaure...

@1/20mpm...................1....................>20mi n
@1/30mpm...................1....................>30mi n
@(1/20+1/30)mpm........1....................>12min : 1/(1/20+1/30)

6. ## Re: Algabaric time messaure...

Or: "one - fill the bath half an hour" fills the bath at the rate of 2 baths per hour.

"the second - fill the bath third of the hour" fills the bath at the rate of 3 baths per hour.

Together, they fill the bath at the rate of 2+ 3= 5 baths per hour.

That is a rate of 1/5 hour per bath or 60/5= 12 minutes to fill one bath.

7. ## Re: Algabaric time messaure...

Think I'll take a shower!

8. ## Re: Algabaric time messaure...

Originally Posted by greg1313
x = time in hours both taps work together

rate 1 = how many baths tap 1 fills in one hour

rate 2 = how many baths tap 2 fills in one hour

1 = the whole job

*** x(rate 1 + rate 2) = 1
How I know the formula (***)?
Why this formula is true?

9. ## Re: Algabaric time messaure...

Originally Posted by policer
How I know the formula (***)?
Why this formula is true?
Are you familiar with

time*rate = distance (quantity)?

10. ## Re: Algabaric time messaure...

O.K.
Why the isn't (1/2+1/3) instead 5...?

11. ## Re: Algabaric time messaure...

Originally Posted by policer
O.K.
Why the isn't (1/2+1/3) instead 5...?
Tap 1 fills the bath in half an hour, or its rate is two full baths per hour.

Tap 2 fills the bath in a third of an hour, or its rate is three full baths per
hour.

12. ## Re: Algabaric time messaure...

Again, why isn't it 1/2 + 1/3...?

13. ## Re: Algabaric time messaure...

Originally Posted by policer
Again, why isn't it 1/2 + 1/3...?
What do you get if you add those? 1/2 hour to fill the bath+ 1/3 hour to fill the bath= 3/6+ 2/6= 5/6 hour per bath, almost an hour. Does it make sense that using both taps it would take longer to fill the bath than only one?

A rate is 'progress (distance, filling a bath, doing a job, whatever) per hour'. You need to invert to get 2 and 3 baths per hour.

14. ## Re: Algabaric time messaure...

Originally Posted by policer
Again, why isn't it 1/2 + 1/3...?
1/2 + 1/3 = 3/6 + 2/6 = 5/6: bath NOT full!
If you're still not satisfied, go take a shower!!