Math Destroyer 2014: help me to understand.

[Daneosaurus]

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Practice test 1, #20.

Justin can paint a fence in 5 hrs, while Austin can paint the same fence in 2 hours, while Gustin can paint the same fence in 2.5 hours. Approximately, how long will it take them if all 3 work together?

A. 50 mins
B. 55 mins
C. 45 mins
D. 1 hr, 5 mins
E. 1 hr, 10 mins

My answer:
(1/5)+(1/2)+(1/2.5)= 11/10 or 1hr, 6 mins (answer choice D is closest)

Destroyer answer:
(1/5)+(1/2)+(1/2.5)= 10/11 or 55 mins

Why does the fraction get flipped????

 

[FeralisExtremum]

Approaching it logically: When you get 11/10, it's because you added the rate at which they work together. So Justin has a rate of 1 fence/ 5 hours , Austin is 1 fence/ 2 hours, Gustin is 1 fence/2.5 hours. that gives a combined rate of 11 fences / 10 hours.

What you want is the amount of time (X hours) it takes them to complete 1 fence. So you set an equality: 11 fences/10 hours = 1 fence / X hours, or simply:

11/10 = 1/X, solve for X.

Another thing you should notice is that if their combined rate is 11 fences in 10 hours, even if you don't know the precise answer, you know they're working at a combined rate faster than 1 fence per hour so the answer must be less than an hour for one fence.

 

[Gutiesc]

First calculate the rate: r= d/t d = distance and we will say the distance is 1 fence

Justin: Austin: Gustin:
1 fence/5 hrs + 1 fence/2 hrs + 1 fence/ 2.5hrs = 11/10 <--- that's the RATE at which they will paint the fence.

Now, we have to look for the TIME they will do it. Adjust the equation for it to give you the time: t=distance / rate Again, distance is 1 fence and the rate is 11/10 so you have t= 1/(11/10) What do you do to get the fraction out of the denominator? you flip and multiply!

1/(11/10) * (10/11) = 10/11

Those use to give me so much trouble until I started watching Chad's VIDEO solutions! He explains tips and tricks so much better than the written form.

 

[qafleshi89]

Daneosaurus,

You worked out the problem perfect. Just a quick look at your work will give your answer. Looking at the ratios, the numerator in the fractions (1 in all three) represents 1 fence and the denominator (5, 2, 2.5) represents the amount of time. As you added all of the fractions you get
(1/5)+(1/2)+(1/2.5)= 11 fences/10 hours.

 

[DrillSoHard]

Your answer was in rate form, they're asking for the time it takes for all of them to paint one fence which is d/r instead of d/t.

 

[Daneosaurus]

Thanks everyone!

 

[CoFe2]

I'm so glad you asked about this one! I've done 4 of those tests now and that is the only one I never fully understood.

 

[adria_justine]

Thank you so much for your explanation, made this more clear for me!