Question

For a certain bathtub, the hot water faucet can fill the tub in 12 minutes. The cold water faucet can fill the tub in 8 minutes. If both faucets are used together, how long will it take to fill the tub

Answer 1

If both faucets are used together, it time taken by them to fill the tub is 4.8 minutes.

What is the concept of time and work?

Time and work share a fundamental idea in common with other arithmetic topics, namely the idea of proportionality.

When the amount of work is constant, efficiency is inversely proportional to the length of time required.

Important Time and Work Formula:

• Work Done = Time Taken × Rate of Work.
• Rate of Work = 1 / Time Taken.
• Time Taken = 1 / Rate of Work.
• If a piece of work is done in x number of days, then the work done in one day = 1/x.
• Total Wok Done = Number of Days × Efficiency.
• Efficiency and Time are inversely proportional to each other.

Calculation for the time taken by both faucet to fill the tub.

The unit should be tub per minute.

Then, do the reciprocal of the result to have minute per tub.

The hot water faucet can fill the tub in 12 minutes.

The cold water faucet can fill the tub in 8 minutes.

The filling rate for both faucets filling the tub at the same time is the sum of their rates.

Let 't' be the time taken by both faucets.

Then,

$\frac{1}{12} +\frac{1}{8} =\frac{1}{t}$

$\frac{8+12}{8*12} =\frac{1}{t}$

$\frac{1}{t} =\frac{20}{96}$

$\frac{t}{1} =\frac{96}{20}$

t = 4.8

Therefore, the time taken by both faucets to fill the tub is 4.8 minutes.

To know more about the formula for calculating power, here

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