Ashley recently opened a store that uses only natural ingredients. She wants to advertise her products by distributing bags of s
amples 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?
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:
<em><u>5.3 hours</u></em>
Explanation:
<u>1) Time it takes Ashley to preprate one bag: </u>
2/3 min
<u>2) Time it takes each friend of Ashley: 75% more than 2/3 min</u>
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
<u>3) Time it takes Ashley and the 4 friends working along to prepare one bag:</u>
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
if x>0 then x+2/x>=3==>x²+2>=3x ==>x²-3x+2>=0 ==>(x-2)(x-1)>=0 positive out of the roots ==> (x<=1 or x>=2) and x>0 ==>(0<x<=1) or (x>=2) else x<0 x+2/x>=3==>x²+2<=3x ==>x²-3x+2<=0 negative betheen the roots ==>(1<=x<=2) and x<0 : no solution end if
