Final answer:
Jennifer and Claire would take approximately 2.92 hours, or 2 hours and 55 minutes, to weed the garden together.
Step-by-step explanation:
To solve this problem, we can use the concept of work rate. Jennifer takes 5 hours to weed the garden, so her work rate is 1/5 (1 job per 5 hours). Claire takes 7 hours to weed the garden, so her work rate is 1/7 (1 job per 7 hours).
When they work together, their work rates add up. So their combined work rate is 1/5 + 1/7 = 12/35 (12 jobs per 35 hours).
To determine how long it would take them to weed the garden together, we can divide the total job (1) by the combined work rate (12/35): 1 ÷ (12/35) = 35/12 ≈ 2.92 hours. Therefore, it would take them approximately 2.92 hours, or 2 hours and 55 minutes, to weed the garden together.