Question

If Dustin does a job in 132 hours and with the help of Ariana they can do it together in 44 hours, how long would it take Ariana to do it alone? _______ hours

a) 66
b) 88
c) 110
d) 132

Answer 1

Ariana's individual work rate is found by subtracting Dustin's work rate (1 job/132 hours) from their combined work rate (1 job/44 hours), resulting in 1 job/66 hours. Therefore, it would take Ariana 66 hours to complete the job alone.

Step-by-step explanation:

To solve this problem, we can assign a work rate to both Dustin and Ariana. If Dustin completes the job in 132 hours, his work rate is 1/132 of the job per hour. When Ariana and Dustin work together, they complete the job in 44 hours, which means their combined work rate is 1/44 of the job per hour.

To find out how long it would take Ariana alone, we need to subtract Dustin's work rate from their combined work rate. Ariana's work rate is (1/44 - 1/132) of the job per hour. To find the time it takes for Ariana to complete the job alone,

1. Calculate the individual work rate of Dustin: 1 job/132 hours.
2. Calculate the combined work rate of Dustin and Ariana: 1 job/44 hours.
3. Subtract Dustin's work rate from the combined work rate to get Ariana's work rate:

(1/44) - (1/132) = (3 - 1)/132 = 2/132 = 1/66

So, Ariana's work rate is 1/66 of the job per hour. To find out how long it would take Ariana to do the job alone, we take the reciprocal of her work rate: 66 hours. Therefore, the correct answer is (a) 66 hours.