Respuesta :
Answer:
The first truck did 62% of all the job.
Step-by-step explanation:
This is the complete problem:
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.
First, from the problem we know that the first truck does its job at a rate per hour: [tex]\frac{1}{5}[/tex]
And, the second truck has a rate per hour of: [tex]\frac{1}{8}[/tex]
So, the rate per hour with both trucks working together will be the sum:
[tex]\frac{1}{5}+\frac{1}{8}=\frac{8+5}{40}=\frac{13}{40}[/tex]
Now, we have to find the time it will take to do the whole job with both trucks, the whole job done will be represented by 100% or 1:
[tex]\frac{13}{40}t=1[/tex]
Where t is the unknown time that it takes to do all the job. Solving this we have:
[tex]t=\frac{40}{13}=3.08[/tex]
This means that the whole job will be done after 3.08 hours using both trucks. However, the problem is asking just about the first truck. To find that answer we just have to multiply its rate with the time:
[tex]\frac{1}{5}3.08=0.62[/tex]
This decimal number represents the portion that the first truck finished to have the job done. 0.62 means that it did 62% of all the job.
