Solving linear equation application

In summary: If you choose to pick 5 hours, you might as well go for 7 hours or 18 hours, as long as the hours are divisible by 3 so that the number of cars washed by everyone is an integer.Working together for 5 hours, the three people will wash 5 + 5 + 6 = 16 cars, meaning they wash 16/5 cars per hour which means they take 5/16 of an hour per car, which is 18.75 minutes. Since we cannot have a fraction of a minute, we would round up to 19 minutes.
  • #1
paulmdrdo1
385
0
each of two brothers can wash a car in 1hr; however, their sister can wash a car in 45min. If the three work together, how long will it take to wash the car?

my solution,

$\frac{1}{60}+\frac{1}{60}+\frac{1}{45}=\frac{1}{x}$

multiply by 36,480x I get

$810x+1215x-36480=1350x$

solving for x I get

$x=18 min.$

can you check my work. thanks! :)
 
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  • #2
I would approach this question using ratios. For each person, I set up the ratio of "proportion of car washed : minutes", giving for each of the boys the ratio 1:60 and for the sister 1:45.

From each of these ratios, we can see that every minute each boy washes 1/60 of the car, and the sister washes 1/45. So if they all worked together, every minute they would wash 1/60 + 1/60 + 1/45 = 2/60 + 1/45 = 1/30 + 1/45 = 3/90 + 2/90 = 5/90 = 1/18 of the car.

So if together they wash 1/18 of the car every minute, then yes, it will take them 18 mins to wash the car.
 
  • #3
I would approach it like this:

Working together for 3 hours the three people can wash 3 + 3 + 4 = 10 cars, meaning they wash 10/3 cars per hour which means they take 3/10 of an hour per car, which is 18 minutes. :D
 
  • #4
MarkFL said:
I would approach it like this:

Working together for 3 hours the three people can wash 3 + 3 + 4 = 10 cars, meaning they wash 10/3 cars per hour which means they take 3/10 of an hour per car, which is 18 minutes. :D

where did you get that 4? :confused:
 
  • #5
paulmdrdo said:
where did you get that 4? :confused:

The sister who washes a car in 45 minutes will wash 4 cars in 3 hours.
 
  • #6
what if they work together for say, 5 hours?

how's that?
 
  • #7
paulmdrdo said:
what if they work together for say, 5 hours?

how's that?

Then they would wash more cars than if they work for 3 hours. (Tongueout)

I chose 3 hours because this is the smallest number of hours resulting in an integral number of cars for everyone, which makes the computation quite simple.
 

FAQ: Solving linear equation application

How do I solve a linear equation application?

To solve a linear equation application, you will need to follow these steps:
1. Identify the variables in the equation and assign them letters.
2. Write out the equation with the variables and constants.
3. Use the appropriate operations (addition, subtraction, multiplication, division) to isolate the variable on one side of the equation.
4. Simplify both sides of the equation until you have a single variable on one side and a numerical value on the other.
5. Check your solution by plugging it back into the original equation to make sure it satisfies the equation.

What is a linear equation application used for?

Linear equation applications are used to solve real-world problems involving linear relationships. They can be used to determine unknown quantities or to find the relationship between two variables.

Can you give an example of a linear equation application?

One example of a linear equation application is calculating the cost of a taxi ride. The cost of a taxi ride can be represented by the equation y = 2.50x + 3, where x is the distance traveled in miles and y is the total cost of the ride. This equation can be used to determine the cost of a specific taxi ride or to compare the costs of different taxi companies.

How are linear equation applications used in science?

Linear equation applications are used in science to model and analyze relationships between variables. They can be used to make predictions, analyze data, and solve problems in fields such as physics, chemistry, and biology.

What is the importance of solving linear equation applications?

Solving linear equation applications is important because it allows us to solve real-world problems and make informed decisions based on mathematical relationships. It also helps us to understand and analyze data and make predictions about future outcomes.

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