Final answer:
Carpenter A will cost less than Carpenter B for any time worked less than 1.43 hours, as calculated by comparing their costs over the same number of hours.
Step-by-step explanation:
To determine for how many hours Carpenter A will cost less than Carpenter B, we need to compare the total cost for each carpenter over the same number of hours. Carpenter A's cost is represented by the equation C(A) = 10 + 15h, where h is the number of hours worked. Carpenter B's cost is simply C(B) = 22h. To find out when Carpenter A is cheaper, we set the equations equal to each other to find the break-even point:
10 + 15h = 22h.
Solving for h, we get:
10 = 22h - 15h,
10 = 7h,
h = 10/7,
h ≈ 1.43 hours.
Therefore, Carpenter A will cost less than Carpenter B for any time worked less than 1.43 hours.