MHB Solving linear equation application

[paulmdrdo1]

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! :)

 

[Prove It]

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.

 

[MarkFL]

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

 

[paulmdrdo1]

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?

 

[MarkFL]

where did you get that 4?

The sister who washes a car in 45 minutes will wash 4 cars in 3 hours.

 

[paulmdrdo1]

what if they work together for say, 5 hours?

how's that?

 

[MarkFL]

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.