Set up the equation which would be used to solve the following problem. Do not actually solve the equation.

Question

Working​ alone, a person A can paint a room in 6 hr. Person B can paint the same room working alone in 7 hr. How long will it take them if they work​ together? (Let t represent the time they work​ together.)
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Part 1
Find an the equation for the time it would take for person A and person B to paint the room together. Choose the correct answer below.
A.one sixth t plus one seventh t equals 1
one sixth t plus one seventh t equals 1
B.one sixth t plus 7 t equals 1
one sixth t plus 7 t equals 1
C.7 t plus 6 t equals 1
7 t plus 6 t equals 1
D.one seventh t plus 6 t equals 1
one seventh t plus 6 t equals 1

Answer 1

To solve the problem, we need to express the rate at which each person works and then combine those rates.

• Person A can complete the job in 6 hours, so their rate is \( \frac{1}{6} \) of the job per hour.
• Person B can complete the job in 7 hours, so their rate is \( \frac{1}{7} \) of the job per hour.

When working together, their combined rate is the sum of their individual rates.

Let \( t \) be the time (in hours) they work together. The equation representing their combined work would be:

\[ \frac{1}{6}t + \frac{1}{7}t = 1 \]

Therefore, the correct choice among the options provided is:

A. \( \frac{1}{6}t + \frac{1}{7}t = 1 \)