Question

working alone, marla can pick forty bushels of apples in 14 hours. one day her friend isabella helped her. it only took them 6.74 hours to pick the forty bushels of apples. how long would it take isabella to do it alone?

10.88 hours

12.83 hours

13 hours

13.54 hours

Explanation:

Step1: Find Marla's work - rate

Marla can pick forty bushels in 14 hours. Her work - rate $r_{M}$ is $\frac{1}{14}$ of the job per hour (since the work rate is the fraction of the job completed per unit of time).

Step2: Find the combined work - rate

Together, Marla and Isabella can pick forty bushels in 6.74 hours. Their combined work - rate $r_{C}$ is $\frac{1}{6.74}$ of the job per hour.

Step3: Let Isabella's work - rate be $r_{I}$

We know that the combined work - rate is the sum of their individual work - rates, so $r_{C}=r_{M}+r_{I}$. Then $r_{I}=r_{C}-r_{M}$.
Substitute the values: $r_{I}=\frac{1}{6.74}-\frac{1}{14}$.
First, find a common denominator. The common denominator of 6.74 and 14 is $6.74\times14 = 94.36$.
$\frac{1}{6.74}-\frac{1}{14}=\frac{14}{94.36}-\frac{6.74}{94.36}=\frac{14 - 6.74}{94.36}=\frac{7.26}{94.36}\approx\frac{7.26}{94.36}\approx0.077$.

Step4: Find the time it takes Isabella to complete the job alone

If Isabella's work - rate is $r_{I}$, and the time $t_{I}$ it takes her to complete the job alone is given by $t_{I}=\frac{1}{r_{I}}$.
$t_{I}=\frac{1}{\frac{7.26}{94.36}}=\frac{94.36}{7.26}\approx13$ hours.

Answer:

13 hours