At a regular hourly rate, Don had estimated that labor cost of a repair job as $336 and he was paid that amount. However, the job took 4hrs longer that he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate, What was the time Don had estimated for the job, in hours?
(a)28
(b)24
(c)16
(d)14
(e)12
OG - Q.137
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Algebraic Approach:neeg wrote:At a regular hourly rate, Don had estimated that labor cost of a repair job as $336 and he was paid that amount. However, the job took 4hrs longer that he had estimated and, consequently, he earned $2 per hour less than his regular hourly rate, What was the time Don had estimated for the job, in hours?
(a)28
(b)24
(c)16
(d)14
(e)12
Let us assume that the regular hourly rate = R, and the estimated time = T
Then RT = 336 ... Equation (1)
Also, (R - 2)(T + 4) = 336 ... Equation (2)
From Equations (1) and (2), RT = (R - 2)(T + 4)
Solving we get, RT = RT - 2T + 4R - 8
T = 2R - 4
Now we can plug in answer choices for T and get the value of R. The option which gives the product of RT as 336 will be the correct answer.
It can be seen that answer choice B is the correct one, since T = 24, R = 14 implies RT = 14 * 24 = 336
The correct answer is B.
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hard to understand why this equation is not good enough
let x be the expected no of hours
336/x-336/(x+4) = 2
x^2+4x-672=0
let x be the expected no of hours
336/x-336/(x+4) = 2
x^2+4x-672=0
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This equaltions is equally good enough.vipulgoyal wrote:hard to understand why this equation is not good enough
let x be the expected no of hours
336/x-336/(x+4) = 2
x^2+4x-672=0
Factoring the above equation you get: (x+28)(x-24)=0; which clearly gives us x=24.
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As stated by Abhishek this equation is good enough for those who are fairly good at algebra.vipulgoyal wrote:hard to understand why this equation is not good enough
let x be the expected no of hours
336/x-336/(x+4) = 2
x^2+4x-672=0
If someone feels it is a bit difficult to factorize the expression, here is a trick...
--> (x² + 4x - 672) = 0
--> (x² + 4x + 4) - 676 = 0
--> (x + 2)² = 676 = 26²
--> (x + 2) = ±26
Hence, x = 24 or x = -28
As x must be positive, x = 24
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