Word problem intermediate algebra

Question

Lou can groom the family dogs in 8 hours and his sister in 5 hours. How long will it take to groom them by working together

Answer 1

“Working together” problems present rates in a way that may seem a little awkward – they use hours per mile instead of miles per hour.  For grooming dogs, we use dogs per hour instead of hours per dog.

PLZ realize that for two people working together, the required time will be more than half the fastest time and less than half the slowest time.  For a problem with 5 and 8 hours, for example, we would expect a combined time somewhere between 2.5 and 4 hours.

 

Working alone, Lou can groom 1/8-th of the family dogs in an hour.

Working alone, his sister can groom 1/5-th of the family dogs in an hour.

 

Working together, the two of them can groom (1/8 + 1/5)-th of the family dogs in an hour.

      (1/8 + 1/5)

      (5/40 + 8/40)

     (13/40)

 Working together, they can groom (13/40)-ths of the family dogs in 1 hour.

 

Inverting this number, we find that it takes (40/13) hours to groom all of the family dogs.

      (40/13)

      3 1/13 hours    (approximately 3.08 or 3 hours 4.6 minutes)

Answer 2

Time taken = 13 / 2 = 6.5 hours