Question

working alone, mikayla can mop the warehouse in ten hours. cody can mop the same warehouse in eight hours. how long would it take them if they worked together?
3.49 hours
4.37 hours
4.44 hours
5.48 hours

Explanation:

Step1: Calculate individual work - rates

Mikayla's work - rate is $\frac{1}{10}$ of the warehouse per hour (since she can complete 1 warehouse in 10 hours). Cody's work - rate is $\frac{1}{8}$ of the warehouse per hour (since he can complete 1 warehouse in 8 hours).

Step2: Calculate combined work - rate

The combined work - rate of Mikayla and Cody is $\frac{1}{10}+\frac{1}{8}=\frac{4 + 5}{40}=\frac{9}{40}$ of the warehouse per hour.

Step3: Calculate the time taken when working together

Let $t$ be the time taken when they work together. Since work = rate×time and the work is 1 warehouse, we have $\frac{9}{40}t = 1$. Solving for $t$, we get $t=\frac{40}{9}\approx4.44$ hours.

Answer:

4.44 hours