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?

Question

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.