Question

Jewel and Angelina together can paint a hall in 6 days. Jewel alone can paint it in 8 days. In how many days can Angelina alone paint it?

• A. 24
• B. 14
• C. 48
• D. 16

Answer 1

Answer:

A. 24

The correct answer is Option A (24 days).

Step-by-Step Solution

1. Find the daily work rates:

   • Together (Jewel + Angelina): They finish in 6 days, so in one day they do $1/6$ of the work.

   • Jewel alone: She finishes in 8 days, so in one day she does $1/8$ of the work.

2. Calculate Angelina's daily work rate:
   To find Angelina's rate, subtract Jewel's rate from their combined rate:
   $\text{Angelina's Rate} = \frac{1}{6} - \frac{1}{8}$

3. Solve the fraction:
   Find a common denominator (which is 24):
   $\frac{4}{24} - \frac{3}{24} = \mathbf{\frac{1}{24}}$ This means Angelina finishes $1/24$ of the hall every day.

4. Find the total days:
   If she does $1/24$ of the work per day, she will need 24 days to finish the whole hall.