# one more question?

Solve: It takes Danny 1 h to milk all of the cows, and it takes his sister 1.5 h. How long will it take to do the job together?

Relevance
• Anonymous

Danny works at the rate of 1 "job" per hour. Danny's sister works at the rate of 1 job per 1.5 hours, or 1/1.5 jobs-per-hour. So after a certain fraction of an hour, say "t" hours, Danny does (1 job / 1 hour)*t of the job and his sister does (1 job / 1.5 hours)*t of the job. You want these fractions to equal one whole job together, so:

(1 job / 1 hr)*t + (1 job / 1.5 hr)*t = 1 job

t + (1/1.5)t = 1

t(1 + 1/1.5) = 1

t(1 + 10/15) = 1

t(15/15 + 10/15) = 1

t(25/15) = 1

t = 15/25 = 3/5

3/5 of an hour is the same as 36/60 of an hour, or 36 minutes.

• Anonymous

Danny works 1.5 times as fast as his sister.

Together they work 1 + 1.5 = 2.5 times as fast as the sister.

They therefore take 1.5/2.5 = 3/5hr = 3*60/5 = 36min.

• Anonymous

Tricky, aren't you? The 40 minutes is a good answer--giving them a moment or two to talk. You could say 37 1/2--but that's not practical.

how many cows.... take 2.5 hours( i plus 1.5) and multiply by the ammount of cows. should work