Question

The city just assigned a second garbage truck to empty the bins in Kat’s neighborhood on trash day. The crew from the first garbage truck used to empty all the bins by themselves in 5 hours. In their training, it took the crew from the second garbage truck 8 hours to empty all the bins. When the two crews start working together, what part of all the garbage bins will the first garbage truck empty? To the nearest tenth, the first garbage truck will empty about of all the bins.

Answer 1

Let n =  total number of bins.

1st truck:
Working rate = (n bins)/(5 hr) = n/5 bins/hr
2nd truck:
Working rate = (n bins)/(8 hr) = n/8 bins/hr

Let x hours be required when both trucks work together. Then
(n/5 + n/8)*x =n
(1/5 + 1/8)x = 1
(13/40)x = 1
x = 40/13 hours.

Amount emptied by 1st truck when working together is
(n/5 bins/hr)*(40/13 hr) = (40/65)n = 61.5% of n

Answer: 61.5% (nearst tenth)

Answer 2

answer is 0.6 it ask for the nearest tenth just took the test