Question

13. Ana and Beth do a job together in three hours. Working alone, Ana does the job in 5 hours. How long will it take Beth to do the job alone? a. 3 and 1/3 hours b. 2 and 1/3 hours c. 3 hours d. 7 and 1/2 hours

Answer 1

Answer:  d. 7 and 1/2 hours

Step-by-step explanation:

Given : The time taken by Ana and Beth do a job together = 3 hours

Time taken by Ana to do a job alone = 5 hours

Let t be the time taken by Beth to do a job .

Then, According to the question ,we have

$\dfrac{1}{3}=\dfrac{1}{5}+\dfrac{1}{t}\\\\ \dfrac{1}{t}=\dfrac{1}{3}-\dfrac{1}{5}\\\\ \dfrac{1}{t}=\dfrac{5-3}{15}=\dfrac{2}{15}\\\\ t=\dfrac{15}{2}=7\dfrac{1}{2}$

i.e.  Time taken by Beth to do a job = $7\dfrac{1}{2}\ hours$

Hence, the  time taken by Beth to do a job alone =  7 and 1/2 hours