Ade alone can complete a job in 12 days. Bayo alone can complete the same job in 18 days. If both of them work together, in how many days would the job be completed?
Explanation
To determine how many days Ade and Bayo will take to complete the job together, follow these steps:
1. Calculate Individual Work Rates:
- Ade's work rate is \(\frac{1}{12}\) of the job per day.
- Bayo's work rate is \(\frac{1}{18}\) of the job per day.
2. Combine Their Work Rates:
- Together, their combined work rate is:
\[
\frac{1}{12} + \frac{1}{18}
\]
3. Find a Common Denominator:
- The least common multiple of 12 and 18 is 36. Thus:
\[
\frac{1}{12} = \frac{3}{36}
\]
\[
\frac{1}{18} = \frac{2}{36}
\]
\[
\frac{1}{12} + \frac{1}{18} = \frac{3}{36} + \frac{2}{36} = \frac{5}{36}
\]
4. Calculate the Time Taken Together:
- If their combined work rate is \(\frac{5}{36}\) of the job per day, then the total time required to complete the job is the reciprocal of this rate:
\[
\text{Time} = \frac{36}{5} = 7.2 \text{ days}
\]
Ade and Bayo, working together, will complete the job in 7.2 days.
The correct answer is B. 7.2 days.
