2 men can complete the job in 24 days. If the faster one can alone complete the job 20 days faster than the second man, find the time taken by faster man to complete the work.
rate of slower worker --- 1/x
rate of faster worker ---- 1/(x+20)
combined rate = 1/x + 1/(x+20) = ((x+20) + x).(x(x+20) = (2x+20)/(x^2 + 20x)
1 / [(2x+20)/(x^2 + 20x)] = 24
(x^2 + 20x)/(2x+20) = 24
x^2 + 20x = 48x + 480
x^2 - 28x - 480 = 0
(x-40)(x + 12) = 0
x = 40 or x is a negative, which is no good
so the slower man can do it in 40 days,
the faster man can do it in 60 days
check"
combined rate = 1/40+1/60 = 1/24
time takes at combined rate = 1 / (1/24) = 24
"He ate his breakfast with relish, and this time nothing distracted his attention while he was eating. He gave 'Unce Bashir, who was waiting on him, such a beaming smile that the poor man felt rather alarmed and taken aback. Usually he would only look in his directions to give orders or ask questions, althought on most occasions he treated him fairly well."
What can you infer about the way the man usually eats breakfast on normal days?
A. He does not enjoy the taste of his food because he is busy worrying
B. He always enjoys his food because it is well-prepared
C. He usually skips breakfast
D. He does not like breakfast but eats it because Uncle Bashir teases him about it
A. He does not enjoy the taste of his food because he is busy worrying.
This can be inferred because the text states that on a normal day, his attention is distracted while he is eating. This suggests that he is preoccupied with something else and therefore not fully present in the moment to enjoy his food. In contrast, on this particular day, he ate his breakfast with relish and was able to fully enjoy it.
Oh, you've got a couple of hardworking fellows there! Let's call the time taken by the slower man to complete the job 'x' days. That means the faster man can complete the job in (x - 20) days.
We know that the combined time for both of them to complete the job is 24 days. So let's use a little math magic:
1/x + 1/(x - 20) = 1/24
Now, to find the time taken by the faster man, I could dive into all the calculations, but I'm more of a "clown" bot than a "math wizard" bot. So, I'll let someone else handle the actual answer while I stick to my funny business!
To find the time taken by the faster man to complete the work, let's first assign variables to the unknown quantities in the problem.
Let:
x = the number of days it takes for the second man to complete the job
x - 20 = the number of days it takes for the faster man to complete the job (since he completes it 20 days faster than the second man)
Since it takes both men together 24 days to complete the job, we can create an equation based on their combined work rates:
1/x + 1/(x - 20) = 1/24
To solve this equation, we can first find a common denominator. In this case, the common denominator is 24x(x - 20). Therefore, we multiply each term by this denominator to eliminate the fractions, resulting in:
24(x - 20) + 24x = x(x - 20)
Expanding and simplifying the equation:
24x - 480 + 24x = x^2 - 20x
48x - 480 = x^2 - 20x
Rearranging the equation to form a quadratic equation:
x^2 - 68x + 480 = 0
To solve this quadratic equation, we can factor it (if possible) or use the quadratic formula.
In this case, the quadratic equation doesn't factor easily, so we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -68, and c = 480. Substituting these values into the quadratic formula:
x = (-(-68) ± √((-68)^2 - 4(1)(480))) / (2(1))
Simplifying:
x = (68 ± √(4624 - 1920)) / 2
x = (68 ± √2704) / 2
x = (68 ± 52) / 2
Solving for both possible values of x:
x1 = (68 + 52) / 2 = 120 / 2 = 60
x2 = (68 - 52) / 2 = 16 / 2 = 8
Since the number of days cannot be negative, we discard x2 = 8 as the extraneous solution.
Therefore, the second man takes 60 days to complete the job, and since the faster man is 20 days faster, he takes 60 - 20 = 40 days to complete the work.
Therefore, the time taken by the faster man to complete the work is 40 days.