Answer:
5.33 hours
Step-by-step explanation:
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?
Time Ashley takes to prepare one bag = 2/3 min
Time it takes each friend of Ashley to prepare one bag = 75% more than it takes Ashley
= (75% of 2/3 min) + 2/3 min
= (0.75 × 2/3) + 2/3
= (3/4 × 2/3) + 2/3
= 6/12 + 2/3
= 1/2 + 2/3
= (3+4)/6
= 7/6 min
Rate of Ashley and 4 friends preparing 1 bag
Rate Ashley works = 1 bag / (2/3) min
= 3/2 bag/min
Rate each friend of Ashley works = 1 bag / (7/6) min
= 6/7 bag/min
Rate 4 friends of Ashley works
= 4 × 6/7 bag/min
= 24/7 bag/min
Rate of Ashley and 4 friends preparing 1 bag = 3/2 bag/min + 24/7 bag/min
= 3/2 + 24/7
= (21+48)/14
= 69/14 bag/min
Time taken to prepare 1575 bags
= number of bags / number of bags per min
= 1,575 bags / (69/14) bags/min
= 1575 × 14/69
= (1575×14)/69
= 22,050 / 69
= 319.57 min
319.57 min to hours
= 319.57 min / 60 min
= 5.33 hours
