Question

The crew of a garbage truck takes 5 hours to empty all the bins in one neighborhood on pickup day. The city assigned a second garbage truck to this neighborhood. During their training, it took the crew from the second truck 8 hours to empty all the bins

Answer 1

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: $\frac{1}{5}$

And, the second truck has a rate per hour of: $\frac{1}{8}$

So, the rate per hour with both trucks working together will be the sum:

$\frac{1}{5}+\frac{1}{8}=\frac{8+5}{40}=\frac{13}{40}$

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:

$\frac{13}{40}t=1$

Where t is the unknown time that it takes to do all the job. Solving this we have:

$t=\frac{40}{13}=3.08$

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:

$\frac{1}{5}3.08=0.62$

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.

Answer 2

Answer:

I think here is the complete question.

https://www.chegg.com/homework-help/questions-and-answers/city-assigned-second-garbage-truck-empty-bins-kat-s-neighborhood-trash-day-crew-first-garb-q24664615

To the nearest tenth the first garbage truck will empty about $= 0.6\ Or\ 61.5 \%$ of all the bins.

Step-by-step explanation:

Lets assign $1$ to the whole work done by both the trucks.

Now part of work done by the first truck $=\frac{1}{5}$ of the whole in terms of hours.

And part of work done by the second truck $=1/8$ of the whole in terms of hours.

Then say that the time taken by both the trucks $=t\ hrs$

Then we can say that

$t(\frac{1}{5} + \frac{1}{8})= 1$ is the time taken to complete the whole work when both crew started working together.

So from here we can calculate $(t)$ in hours both of the crews have taken to finish the job.

$t\times(\frac{1}{5} + \frac{1}{8})= 1$

$t\times(\frac{13}{40})= 1$

$t=(\frac{1\times 40}{13})$

$t=(\frac{40}{13})$ hrs.

So we can say that both the trucks work for  $\frac{40}{13}$ hrs.

Now as we have already assumed that the part of work done by first truck $=\frac{1}{5}$

So $\frac{1}{5}$ of the total $t$

$=\frac{1}{5} \times \frac{40}{13} =\frac{40}{65}= 0.615\approx 0.6$ work of the whole.

Which in terms of percentage can be written as $=0.615\times 100 =61.5\%$

Now we can say that the first garbage truck will work $61.5\%$ of the entire job or $\frac{40}{65}$ of the whole work.