# Percentage questions

#### leomac

##### New member
Hello everyone I have a problem:
I have to calculate how much each car contributes as a percentage to give me a total spending balance in $, in a given rental period calculated as a percentage. For example: Car 1: spending balance 2000$, on 75% of the time of which it was rented;
Car 2: spending balance 2000 $, on 55% of the time of which it was rented; total spending balance 4000$, on 100% of the time of which the cars were rented.

The cars can be used at the same time.

How much each car has contributed in percentage to give me the total balance spent, based on the time of rent in percentage?

It should be the second by eye and cross but I cannot calculate it. I'm going crazy, could you help me?

#### leomac

##### New member
Perhaps with this other example it is easier to understand what I have to do.

Jhon and Robert are two workers. They have to fill a tank.
Jhon transports and fills the tank with 2 liters of water. Then exhausted he goes home.
Robert transports and fills the tank with another 2 liters of water. Then he too exhausted goes home.

In 100% of the time (it does not matter if it's a year, a month, a day, ...) Jhon fills the tank in 75%, Robert in 55%.

If I have $100, how much do I pay Jhon and Robert considering the time they took to do their job (the impact on total)? Robert took less time, so he should get paid more because he carried more water in less time. But I can not calculate how much I have to pay him. #### leomac ##### New member #### Denis ##### Senior Member It should be the second by eye and cross but I cannot calculate it. I'm going crazy, could you help me? I'm also going crazy trying to understand that! "by eye and cross" #### HallsofIvy ##### Elite Member "crossed eyes"? #### Dr.Peterson ##### Elite Member Perhaps with this other example it is easier to understand what I have to do. Jhon and Robert are two workers. They have to fill a tank. Jhon transports and fills the tank with 2 liters of water. Then exhausted he goes home. Robert transports and fills the tank with another 2 liters of water. Then he too exhausted goes home. In 100% of the time (it does not matter if it's a year, a month, a day, ...) Jhon fills the tank in 75%, Robert in 55%. If I have$ 100, how much do I pay Jhon and Robert considering the time they took to do their job (the impact on total)?

Robert took less time, so he should get paid more because he carried more water in less time. But I can not calculate how much I have to pay him.
Please explain what that means. 75% of what? And do you know anything at all about how much time each spent? And why must you pay for their time, rather than the work done (which appears to be the same for each)?

#### leomac

##### New member
Hi and thanks for the reply. Sorry for the delay but I received the notification now.

The percentage is the time. 75% is the time which Jhon takes to fill the tank, 100% is the total time. For example if 100% is one year, 50% are six months. But in this circumstance it does not interest to me, 100% should be an year or a minute.

I have to pay them in according to the effort which they do during the job. In this case I think that this effort should be the speed of filling. So I tried to do the following:

TOTAL time 100%
Mark 2L in 75% of the time (t) ==> 1% t : x L = 75% t : 2 L => 0.02 L in 1% of the time

Jhon 3L in 60% of the time (t) ==> 1% t : x L = 60% t : 3 L => 0.05 L in 1% of the time
Victor 2L in 33% of the time (t) ==> 1% t : x L = 33% t : 2 L => 0.06 L in 1% of the time

0.02L + 0.05L + 0.06L = 0.13 L TOT at 1% of the time

Mark => 0.02 L : 0.13 TOT L = x : 100 => 15.4 %
Jhon => 0.05 L : 0.13 TOT L = x : 100 => 38.5 %
Victor => 0.05 L : 0.13 TOT L = x : 100 => 46.1 %

So if I've 100$, I give 46.1$ to Victor, 38.5$to Jhon and 15.4$ to Mark.
Is it correct? Thaks

#### leomac

##### New member
I'm also going crazy trying to understand that! "by eye and cross"
Sorry bad translation... I meant "A rough guess", "If I had any guess,".

"If I had any guess, It should be the second but I cannot calculate it."

Anyone?

#### Dr.Peterson

##### Elite Member
The percentage is the time. 75% is the time which Jhon takes to fill the tank, 100% is the total time. For example if 100% is one year, 50% are six months. But in this circumstance it does not interest to me, 100% should be an year or a minute.

I have to pay them in according to the effort which they do during the job. In this case I think that this effort should be the speed of filling. So I tried to do the following:

TOTAL time 100%
Mark 2L in 75% of the time (t) ==> 1% t : x L = 75% t : 2 L => 0.02 L in 1% of the time

Jhon 3L in 60% of the time (t) ==> 1% t : x L = 60% t : 3 L => 0.05 L in 1% of the time
Victor 2L in 33% of the time (t) ==> 1% t : x L = 33% t : 2 L => 0.06 L in 1% of the time

0.02L + 0.05L + 0.06L = 0.13 L TOT at 1% of the time

Mark => 0.02 L : 0.13 TOT L = x : 100 => 15.4 %
Jhon => 0.05 L : 0.13 TOT L = x : 100 => 38.5 %
Victor => 0.05 L : 0.13 TOT L = x : 100 => 46.1 %

So if I've 100$, I give 46.1$ to Victor, 38.5$to Jhon and 15.4$ to Mark.
Is it correct?
I'd think you'd want to pay for the work done, not for speed, because that is what benefits you. If you pay each of them the same for the same number of liters, then the one who is faster is getting more per hour, which is appropriate.

I also think it's confusing to measure time in percent rather than just in days or years or whatever, since you are talking about a fixed time, not about a percentage of the total time they take (despite your use of the word "total").

I can't make much sense of your calculation. Let's take it this way:

Suppose Mark transports 2 liters in 0.75 hour, John 3 liters in 0.60 hour, and Victor 2 liters in 0.3 hour. Since the total amount filled is 2+3+2 = 7 liters, I'd pay them, respectively, 2/7, 3/7, and 2/7 of the \$100. It makes sense for John to get more, because he has done more for you.

Their rates are:

Mark: 2/0.75 = 2.66 liters/hour
John: 3/0.60 = 5 liters/hour
Victor: 2/0.33 = 6 liters/hour

If you paid them in proportion to their rates (which is true of the amounts you calculated), you would pay Victor more than John, though he accomplished less and spent less time working for you. Why?

Or do you really want to somehow combine rate and work done, giving a bonus for speed?

#### leomac

##### New member
I would first like, I am not a manger nor a businessman and this is just an example that can be applied to cars, to rents and their impact on the total net or to the children who build a tower with Lego and as a reward I give them some chocolate.

If you paid them in proportion to their rates (which is true of the amounts you calculated), you would pay Victor more than John, though he accomplished less and spent less time working for you. Why?

Or do you really want to somehow combine rate and work done, giving a bonus for speed?
Because if you see the impact of the worker on the system you realize that Victor made more than others. In particular, he made 46% of the work compared to Jhon with 38% but above all to Mark that he made only 15%.

This makes me realize how much time it takes to actually do that work and above all to Mark that is out of trend on who I have to focus.
The activity does not take 0.02 L in 1% of the time but more or less, we are at 0.05 / 0.06 L in 1% of the time and they have to be paid for that. Consider that usually a worker is paid according to working time and not to the effort made or how much he impacts the system in which he is working, so I must bring Mark into line.

Thanks at all for the clarification.