Question

Ashley recently opened a store that uses only natural ingredients. She wants to advertise her products by distributing bags of samples in her neighborhood. It takes Ashley \dfrac{2}{3} 3 2 ​ start fraction, 2, divided by, 3, end fraction of a minute to prepare one bag. It takes each of her friends 75\%75%75, percent longer to prepare a bag. How many hours will it take Ashley and 444 of her friends to prepare 157515751575 bags of samples?

Answer 1

I will rewrite the question for better understanding:

Ashley recently opened a store that uses only natural ingredients. She wants to advertise her products by distributing bags of samples in her neighborhood. It takes Ashley 2/3 of a minute to prepare one bag. It takes each of her friends 75% longer to prepare a bag. How many hours will it take Ashley and 4 of her friends to prepare 1575 bags of samples?

Answer:

• 5.3 hours

Explanation:

1) Time it takes Ashley to preprate one bag:

• 2/3 min

2) Time it takes each friend of Ashley: 75% more than 2/3 min

• 75% × 2/3 min = 0.75 × 2/3 min = 3/4 × 2/3 min= 2/4 min = 1/2 min = 0.5 min

• 2/3 min + 1/2 min = 7/6 min

3) Time it takes Ashley and the 4 friends working along to prepare one bag:

• Convert each time into a rate, since you can set that the total rate of Ashley along with her four friends is equal to the sum of each rate:

• Rate of Ashley: 1 bag / (2/3) min = 3/2 bag/min

• Rate of each friend: 1 bag / (7/6) min = 6/7 bag/min

• Rate of Ashley and 4 friends = 3/2 bag/min + 4 × 6/7 bag/min = (3/2 +24/7) bag/min = 69/14 bag/min

4) Time of prepare 1575 bags of samples:

• time = number of bags / number of bags per min = 1,575 bags / (69/14) bags/min = 319.56 min

5) Convert minutes to hours:

• 356.56 min × 1 hour / 60 min = 5.3 hours