Math Destroyer Question

[Chubz0924]

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I am having trouble figuring out how to set up Question 20 from practice test 1 on destroyer: Justin can paint a fence in 5 hours, while Austin can paint the same fence in 2 hours, while Gustin can paint it in 2.5 hours. Approx, how long will it take them if all three work together?

 

[helloboys]

(1/5)+(1/2.5)+(1/2)=(1/T)
0.20+0.4+0.5=(1/T)
1.1=(1/T)
T=0.9 or 54 mins

 

[artist2022]

Combined work problems are set up like this: 1/A + 1/B + 1/C = 1/T
So, you use the time it takes for each of them to work by themselves (J=5, A=2, G=5/2)
Now, you plug these into the equation, and solve for T: the total time it would take if they worked together
(1/5) + (1/2) + (1/(5/2)) = 1/T
Solving for T, you get: 1/T = 11/10. Flip it, and now you get T = 10/11. But remember, this is in hours. So, you multiply by 60 to convert to minutes, and you get approx 55min. Hope this helps 🙂

 

[Chubz0924]

Combined work problems are set up like this: 1/A + 1/B + 1/C = 1/T
So, you use the time it takes for each of them to work by themselves (J=5, A=2, G=5/2)
Now, you plug these into the equation, and solve for T: the total time it would take if they worked together
(1/5) + (1/2) + (1/(5/2)) = 1/T
Solving for T, you get: 1/T = 11/10. Flip it, and now you get T = 10/11. But remember, this is in hours. So, you multiply by 60 to convert to minutes, and you get approx 55min. Hope this helps 🙂

Thank you, this really helps a lot. The only part I am lost at is how do you get 11/10?

 

[artist2022]

Thank you, this really helps a lot. The only part I am lost at is how do you get 11/10?

(1/5) + (1/2) + (1/(5/2)) = 1/T
(1/5) + (1/2) + (2/5) = 1/T
(3/5) + (1/2) = 1/T
(6/10) + (5/10) = 1/T
(11/10) = 1/T.
You then flip these two, and you get 10/11 = T/1 (which is just T). So, T = 10/11 hours, aka 54 min.