Question

It takes Sue, Jeff and Todd 4 hours to paint a room together. If it takes Sue 10 hours by herself and Jeff 12 hours by himself, how long would it take Todd to paint the room alone?

Answer 1

The number of time it would take Todd to paint the room alone is 15 hours.

• Let the Todd's time be t.

Given the following data:

• Combine time = 4 hours

• Sue's time = 10 hours

• Jeff's time = 12 hours

To calculate the number of time it would take Todd to paint the room alone:

How to solve a word problem:

In order to solve this exercise, we would first of all calculate their individual rate and combined rate respectively. Finally, we would add their individual rates together and equate it to the combined rate.

For Sue:

$Rate = \frac{1}{10} \;work/hr$

For Jeff:

$Rate = \frac{1}{12} \;work/hr$

For Todd:

$Rate = \frac{1}{t} \;work/hr$

Combined rate:

$Rate = \frac{1}{4} \;work/hr$

Adding the individual rates, we have:

$\frac{1}{10} +\frac{1}{12} +\frac{1}{t} =\frac{1}{4}$

Multiplying all through by 120t, we have:

$12t+10t+120=30t\\ \\ 22t+120=30t\\ \\ 120=30t-22t\\ \\ 120=8t\\ \\ t=\frac{120}{8}$

t = 15 hours.

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