Question

Ana and Beth do a job together in two hours. Working alone, Ana does the job in 5 hours. How long will it take Beth to do the job alone?
3 hours
2 hours
3 1/3 hours
2 1/3 hours

By how much is 35% of P220 greater than 55% of P140?
P 16.00
P 20.00
P 480,000
P 0.00

Answer 1

To solve these problems, we'll tackle them one at a time.

### Problem 1: Ana and Beth working together

1. **Determine rates of work:**
- Ana's rate is \( \frac{1}{5} \) of the job per hour (since she can complete it alone in 5 hours).
- Let Beth's working time be \( x \) hours, then her rate is \( \frac{1}{x} \) of the job per hour.

2. **Find combined rate when they work together:**
- Together, they complete the job in 2 hours, which means their combined rate is \( \frac{1}{2} \) of the job per hour.

3. **Set up the equation:**
\[
\frac{1}{5} + \frac{1}{x} = \frac{1}{2}
\]

4. **Solve for \( x \):**
- First, find a common denominator for the fractions on the left side. The common denominator for 5 and \( x \) is \( 5x \):
\[
\frac{x}{5x} + \frac{5}{5x} = \frac{1}{2}
\]
\[
\frac{x + 5}{5x} = \frac{1}{2}
\]

5. **Cross-multiply:**
\[
2(x + 5) = 5x
\]

6. **Distribute and solve:**
\[
2x + 10 = 5x
\]
\[
10 = 3x
\]
\[
x = \frac{10}{3} \text{ hours} \approx 3.33 \text{ hours or } 3 \frac{1}{3} \text{ hours}
\]

**Therefore, it will take Beth approximately 3 1/3 hours to do the job alone.**

### Problem 2: Find the difference between 35% of P220 and 55% of P140

1. **Calculate 35% of P220:**
\[
0.35 \times 220 = 77
\]

2. **Calculate 55% of P140:**
\[
0.55 \times 140 = 77
\]

3. **Find the difference:**
\[
77 - 77 = 0
\]

**Therefore, 35% of P220 is equal to 55% of P140, so the result is P 0.00.**

### Summary of the Answers:
1. Beth will take **3 1/3 hours** to do the job alone.
2. The difference is **P 0.00**.