Final answer:
Imani and Gabriella working together would have a combined painting rate of 15/56 fences per hour. Therefore, they would take 3.7 hours to paint the fence together when rounded to the nearest tenth.
Step-by-step explanation:
When Imani and Gabriella work together, we need to combine their rates of work to find out how long it will take them to paint the fence together. Imani can paint a fence in seven hours, which means her rate is 1/7 of the fence per hour. Gabriella can paint the same fence in eight hours, so her rate is 1/8 of the fence per hour. To find the combined rate, we add these two rates together:
Combined rate = 1/7 + 1/8.
First, find a common denominator which is 56:
Combined rate = 8/56 + 7/56
Combined rate = (8+7)/56
Combined rate = 15/56 fences per hour.
Now, to find how long it would take them to paint one whole fence:
Total time = 1 / (Combined rate)
Total time = 1 / (15/56)
Total time = 56/15
Total time = 3.733...
Therefore, when rounded to the nearest tenth, Imani and Gabriella would take 3.7 hours to paint the fence together.