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Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?
- a)1/3x
- b)3x/(x – 3)
- c)(x – 3) / 3x
- d)x / (x – 3)
- e)(x – 3) / x
Correct answer is option 'C'. Can you explain this answer?
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Lindsay can paint 1/x of a certain room in 20 minutes. What fraction o...
We can solve this problem as a VIC (Variable In answer Choice) and plug in values for the variable x. Let’s say x = 6. (Note that there is a logical restriction here in terms of the value of x. Lindsay has to have a rate of less than less than 1 room per hour if she needs Joseph’s help to finish in an hour).
If Lindsay can paint 1/6 of the room in 20 minutes (1/3 of an hour), her rate is 1/2.
rt = w
r(1/3) = 1/6
r = 1/2
rt = w
r(1/3) = 1/6
r = 1/2
Let J be the number of hours it takes Joseph to paint the entire room. Joseph’s rate then is 1/J. Joseph and Lindsay’s combined rate is 1/2 + 1/J, which can be simplified:
1/2 + 1/J → J / 2J + 2 / 2J → (J + 2) / 2J
1/2 + 1/J → J / 2J + 2 / 2J → (J + 2) / 2J
If the two of them finish the room in one hour, using the formula of rt = w, we can solve for J.
rt = w and t = 1 (hour), w = 1 (job)
((J + 2) / 2J )(1) = 1 → J + 2 = 2J → J =2
That means that Joseph’s rate is 1/2, the same as Lindsay’s. The question though asks us what fraction of the room Joseph would complete in 20 minutes, or 1/3 of an hour.
rt = w
(1/2)(1/3) = w
w = 1/6
rt = w and t = 1 (hour), w = 1 (job)
((J + 2) / 2J )(1) = 1 → J + 2 = 2J → J =2
That means that Joseph’s rate is 1/2, the same as Lindsay’s. The question though asks us what fraction of the room Joseph would complete in 20 minutes, or 1/3 of an hour.
rt = w
(1/2)(1/3) = w
w = 1/6
Now we must look at the answer choices to see which one is equal to 1/6 when we plug in x = 6. Only C works: (6 – 3) / 18 = 1/6.
The correct answer is C.
Most Upvoted Answer
Lindsay can paint 1/x of a certain room in 20 minutes. What fraction o...
Let's start by finding Lindsay's rate of painting the room:
Lindsay can paint 1/x of the room in 20 minutes, so her rate is 1/(20x) of the room per minute.
Let's call Joseph's rate of painting the room y. Then his rate is y/(20) of the room per minute.
Working together, their combined rate is 1/60 of the room per minute (since they can paint the entire room in one hour).
So we can set up the equation:
1/(20x) + y/(20) = 1/60
To solve for y, we need to get rid of the fractions. Multiplying both sides by 60x, we get:
3x + 3y = x
Simplifying, we get:
y = (x/3) - x
y = -2x/3
So Joseph's rate of painting the room is -2x/60, or -1/(30x) of the room per minute.
In 20 minutes, Joseph can paint (-1/(30x))*20 = -2/3x of the room. But we're looking for a fraction, so we'll take the absolute value and simplify:
|(-2/3x)| = 2/3x
So the answer is (b) 3x/(2x), which simplifies to 3/2.
Lindsay can paint 1/x of the room in 20 minutes, so her rate is 1/(20x) of the room per minute.
Let's call Joseph's rate of painting the room y. Then his rate is y/(20) of the room per minute.
Working together, their combined rate is 1/60 of the room per minute (since they can paint the entire room in one hour).
So we can set up the equation:
1/(20x) + y/(20) = 1/60
To solve for y, we need to get rid of the fractions. Multiplying both sides by 60x, we get:
3x + 3y = x
Simplifying, we get:
y = (x/3) - x
y = -2x/3
So Joseph's rate of painting the room is -2x/60, or -1/(30x) of the room per minute.
In 20 minutes, Joseph can paint (-1/(30x))*20 = -2/3x of the room. But we're looking for a fraction, so we'll take the absolute value and simplify:
|(-2/3x)| = 2/3x
So the answer is (b) 3x/(2x), which simplifies to 3/2.
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Lindsay can paint 1/x of a certain room in 20 minutes. What fraction of the same room can Joseph paint in 20 minutes if the two of them can paint the room in an hour, working together at their respective rates?a)1/3xb)3x/(x – 3)c)(x – 3) / 3xd)x / (x – 3)e)(x – 3) / xCorrect answer is option 'C'. Can you explain this answer?
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