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Ted can finish a job in 3 hours and Ann can finish the same job in 4 h
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14 Feb 2022, 08:00
14 Feb 2022, 08:00
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Question Stats:
85% (01:50) correct
14% (03:21) wrong based on 14 sessions
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Ted can finish a job in 3 hours and Ann can finish the same job in 4 hours. If Ted works alone for 1 hour, and then Ann and Ted work together to finish the job, for how many more hours do they have to work together?
(A) 8/7
(B) 6/5
(C) 5/4
(D) 4/3
(E) 3/2
(A) 8/7
(B) 6/5
(C) 5/4
(D) 4/3
(E) 3/2
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Re: Ted can finish a job in 3 hours and Ann can finish the same job in 4 h
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24 Feb 2022, 01:13
24 Feb 2022, 01:13
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Carcass wrote:
Ted can finish a job in 3 hours and Ann can finish the same job in 4 hours. If Ted works alone for 1 hour, and then Ann and Ted work together to finish the job, for how many more hours do they have to work together?
(A) 8/7
(B) 6/5
(C) 5/4
(D) 4/3
(E) 3/2
(A) 8/7
(B) 6/5
(C) 5/4
(D) 4/3
(E) 3/2
Let they work for \(x\) hours together.
Rate of Ted = \(\frac{1}{3}\), and
Rate of Ann = \(\frac{1}{4}\)
Now, Total work done by both Ted and Ann must be 1
i.e. \(W_T + W_A = 1\)
Since, Work = (Rate)(Time)
We can write the above equation as;
\((R_T)(T_T) + (R_A)(T_A) = 1\)
Now, Ted worked for a total of \((1 + x)\) hours i.e. \(T_T = (1 + x)\)
whereas, Ann worked for a total of \(x\) hours i.e. \(T_A = x\)
\(\frac{1}{3}(1 + x) + \frac{1}{4}(x) = 1\)
\(\frac{1}{3} + \frac{x}{3} + \frac{x}{4} = 1\)
\(\frac{x}{3} + \frac{x}{4} = \frac{2}{3}\)
\(\frac{4x + 3x}{12} = \frac{2}{3}\)
\(\frac{7x}{12} = \frac{2}{3}\)
\(x = \frac{8}{7}\)
Hence, option A
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Ted can finish a job in 3 hours and Ann can finish the same job in 4 h
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24 Feb 2022, 06:37
24 Feb 2022, 06:37
2
Carcass wrote:
Ted can finish a job in 3 hours and Ann can finish the same job in 4 hours. If Ted works alone for 1 hour, and then Ann and Ted work together to finish the job, for how many more hours do they have to work together?
(A) 8/7
(B) 6/5
(C) 5/4
(D) 4/3
(E) 3/2
(A) 8/7
(B) 6/5
(C) 5/4
(D) 4/3
(E) 3/2
Another approach here is to assign a "nice" value to the job, a value that works well with the given information (3 hours and 4 hours).
So, let's say the entire job consists of making 12 widgets.
So, if Ted can finish the job in 3 hours, this means he can make 12 widgets in 3 hours, which means his RATE is 4 widgets per hour.
Similarly, if Ann can finish the job in 4 hours, this means she can make 12 widgets in 4 hours, which means her RATE is 3 widgets per hour
Ted works alone for 1 hour...
Since Ted's RATE is 4 widgets per hour, we know that Ted makes 4 widgets during that 1 hour.
So, the job remaining = 12 - 4 = 8 widgets
...and then Ann and Ted work together to finish the job
Ann and Ted's combined rate = (4 widgets per hour) + (3 widgets per hour) = 7 widgets per hour
How many more hours do they have to work together?
Time = output/rate = 8/7
Answer: A
