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It takes 10 mins to fill a bath with just the hot tap and 15 minutes to fill it just with the cold tap.

How long wikll it take to fill the bath if you run both taps at once?

Please give a equation or the steps of solving, thanks a lot!

1 Answer

6 votes

Answer: 6 minutes

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Step-by-step explanation:

Let's say the tub is 30 gallons. I'm picking this number because it's the LCM of 10 and 15. Picking the LCM means that later division operations result in a whole number.

The hot tap takes 10 minutes to fill the tub. Its rate is 30/10 = 3 gallons per minute.

Rate = (amount done)/(time)

The cold tap works at a rate of 30/15 = 2 gallons per minute.

When both taps are running at the same time, they combine to a total rate of 3+2 = 5 gallons per minute. Therefore, it will take 30/5 = 6 minutes if both taps are opened.

Time = (amount done)/(rate)

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Another approach:

The hot water tap takes 10 minutes to do 1 job. That "1 job" refers to "fill the bathtub". The unit rate here is 1/10 of a job per minute.

Meanwhile, the cold tap has a unit rate of 1/15 of a job per minute.

The combined rate is 1/10 + 1/15 = 3/30+2/30 = 5/30 = 1/6 of a job per minute.

x = number of minutes it takes to fill the bathtub if both taps are going at once.

We can say:

(unit rate)*(time) = amount done

(1/6 of a job per min)*(x minutes) = 1 job

(1/6)x = 1

x = 6 minutes is the final answer

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Another approach:

The template for problems like this is:

1/A + 1/B = 1/C

where

  • A = amount of time for the hot tap water (working alone)
  • B = amount of time for the cold tap water (working alone)
  • C = amount of time if the two taps work together

We end up with the equation

1/10 + 1/15 = 1/x

This can be rearranged into

(1/10+1/15)x = 1

and also rearrange into

(1/6)x = 1

Follow the steps mentioned earlier to end up with 6 minutes as the final answer

User Gael Lorieul
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