Question

Bob and Pat are asked to paint a house. Bob can paint the house by himself in 12 hours and pat can paint by herself in 16 hours. How long would it take to paint the house if they worked together?

Answer 1

Step-by-step explanation:

let total work =48

Bob efficiency = 48/12=4

Pat efficiency = 48/16=3

time = 48/7 hrs.....

Answer 2

Answer:

It takes 48/7 hrs to paint the house if they work together.

Step-by-step explanation:

Assumption,

Let the time taken to paint the house if both the persons worked together to be 't'

Given,

The time takes Bob to paint the house (t1) is 12 hrs.

The time it took Pat to paint the house (t2) was 16 hrs.

To find,

The time is taken to paint the house if both the persons worked together.

Calculation,

If Bob takes 12 hrs to paint 'x' amount of house, then in 1 hr of time Bob paints:

x/12 amount of house.

Also,

If Pot takes 16 hrs to paint 'x' amount of house, then in 1 hr of time Pot paints:

x/16 amount of house.

Similarly,

If Both takes t hrs to paint 'x' amount of house, then in 1 hr of time Both paints:

x/t amount of house.

Now,

x/12 + x/16 = x/t

⇒ 1/12 + 1/16 = 1/t

⇒ (16 + 12)t = 12 × 16

⇒ t = 48/7 = 6.85 hrs.

Therefore, it takes 48/7 hrs to paint the house if they work together.

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