7. Marcus can paint a garage in 3 hours. Gina can paint the same garage in 2 hours. How long will it take Marcus and Gina to paint the garage if they work together
Combined rate
= 1/3 garage/h + 1/2 garage/h
= 5/6 garage/h
5/6 garage/h * T (h) = 1 garage
T = 6/5 h = 1 h, 12 minutes.
To find out how long it will take Marcus and Gina to paint the garage together, we need to calculate their combined painting rate.
We can start by finding Marcus's painting rate. He can paint the garage in 3 hours, which means he can paint 1/3 of the garage in an hour.
Similarly, Gina can paint the garage in 2 hours, so her painting rate is 1/2 of the garage per hour.
To find their combined painting rate, we add their individual rates. So, Marcus and Gina together can paint 1/3 + 1/2 of the garage per hour.
To simplify the calculation, we need to find a common denominator for 3 and 2, which is 6. So, Marcus and Gina together can paint (2/6 + 3/6) of the garage per hour, which equals 5/6.
Now, we know that Marcus and Gina together can paint 5/6 of the garage per hour. To find out how long it will take them to paint the whole garage, we divide 1 (representing the whole garage) by their combined painting rate, 5/6.
Dividing 1 by 5/6 is the same as multiplying 1 by the reciprocal of 5/6, which is 6/5.
Therefore, it will take Marcus and Gina 6/5 hours to paint the garage together. To convert this into the mixed number format:
6/5 hours = 1 hour and 1/5 of an hour
So, Marcus and Gina will take approximately 1 hour and 12 minutes to paint the garage together.