Machines A and B, working together, take t minutes to

Question

Source: Veritas Prep Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work? A. 5:8 B. 8:5 C. 25:64 D. 25:39 E. 64:25 The OA is B

GMATGuruNY · Answer

BTGmoderatorLU wrote:Source: Veritas Prep Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work? A. 5:8 B. 8:5 C. 25:64 D. 25:39 E. 64:25 Always keep your eye on the answer choices. Since A's time alone (t+64) is greater than B's time alone (t+25), the ratio of A's time alone to B's time alone must be GREATER THAN 1. Eliminate A, C and D. Since the ratio of A's time to B's time = (t+64)/(t+25), option E implies the following: (t+64)/(t+25) = 64/25. The resulting equation is valid only if t=0. Not possible. Eliminate E. The correct answer is B.

fskilnik@GMATH · Answer

BTGmoderatorLU wrote:Source: Veritas Prep Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work? A. 5:8 B. 8:5 C. 25:64 D. 25:39 E. 64:25 $${m{times}}\,\,{m{A,}}\,B\,\,\,\,\,\, 	o \,\,\,\,\,\min $$ $$? = {A \over B}$$ $$\left( * ight)\,\,\,\left\{ \matrix{ A = t + 64 \hfill \cr B = t + 25 \hfill \cr} ight.$$ $${1 \over A} + {1 \over B} = {1 \over t}\,\,\,\,\left( {{m{stem}}} ight)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{{1 \cdot B} \over {A \cdot B}} + {{1 \cdot A} \over {B \cdot A}} = {1 \over t}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * ight)} \,\,\,\,\,{{2t + 89} \over {\left( {t + 64} ight)\left( {t + 25} ight)}} = {1 \over t}$$ $$2{t^2} + 89t = {t^2} + 89t + 25 \cdot 64\,\,\,\,\,\,\mathop \Rightarrow \limits^{t\,\, > \,\,0} \,\,\,\,\,t = 5 \cdot 8 = 40$$ $$?\,\,\,\mathop = \limits^{\left( * ight)} \,\,\,{{40 + 64} \over {40 + 25}}\,\, = \,\,{{104:13} \over {65:13}} = {8 \over 5}$$ We follow the notations and rationale taught in the GMATH method. Regards, Fabio.

GMATGuruNY · Answer

BTGmoderatorLU wrote:Source: Veritas Prep Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work? A. 5:8 B. 8:5 C. 25:64 D. 25:39 E. 64:25 One more approach: Since A+B together complete the job in t minutes: Job = (A's output in t minutes) + (B's output in t minutes) If A works alone for t minutes, A can then complete the rest of the job in 64 minutes. In this case, the rest of the job = B's output in t minutes. Thus, A's output in 64 minutes is equal to B's output in t minutes: A/64 = B/t A/B = 64/t If B works alone for t minutes, B can then complete the rest of the job in 25 minutes. In this case, the rest of the job = A's output in t minutes. Thus, A's output in t minutes is equal to B's output in 25 minutes: A/t = B/25 A/B = t/25 The expressions in blue are both equal to A/B and thus must be equal to each other: t/25 = 64/t t² = 25*64 t = 5*8 t = 40 Thus: A's time alone = t+64 = 40+64 = 104 B's time alone = t+25 = 40+25 = 65 (A's time alone) : (B's time alone) = 104:65 = (8*13) : (5*13) = 8:5 The correct answer is B.

Rich.C@EMPOWERgmat.com · Answer

Hi All,

We're told that Machines A and B, working together, take T minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than T to complete the same work. Machine B, working alone, takes 25 minutes more than T to complete the same work. We're asked for the ratio of the time taken by machine A to the time taken by machine B to complete this work. While this question is layered, it's ultimately a "Work Formula" question, so you can use the Work Formula - and a bit of Algebra - to solve it.

Work = (A)(B)/(A+B) where A and B are the individual times needed to complete the task

In this prompt, we have:
A = T + 64
B = T + 25

Substituting in those values, we have:

(T+64)(T+25)/(T+64 + T+25) = T

(T^2 + 89T + 1600)/(2T + 89) = T
T^2 + 89T + 1600 = T(2T + 89)
T^2 + 89T + 1600 = 2T^2 + 89T
1600 = T^2
T = +40 or -40

Since we cannot have a "negative time" for T, we know that T MUST be 40 minutes, meaning that the two individuals times for A and B are:
A = 40 + 64 = 104 minutes
B = 40 + 25 = 65 minutes
A/B = 104/65 = 8/5

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Scott@TargetTestPrep · Answer

BTGmoderatorLU wrote:Source: Veritas Prep Machines A and B, working together, take t minutes to complete a particular work. Machine A, working alone, takes 64 minutes more than t to complete the same work. Machine B, working alone, takes 25 minutes more than t to complete the same work. What is the ratio of the time taken by machine A to the time taken by machine B to complete this work? A. 5:8 B. 8:5 C. 25:64 D. 25:39 E. 64:25 The OA is B We can let a = the number of minutes A can finish the work by itself and b = the number of minutes B can finish the work by itself. Thus, their rates are 1/a and 1/b, respectively. We can create the equations: t(1/a) + t(1/b) = 1 (t + 64)(1/a) = 1 and (t + 25)(1/b) = 1 From the second and third equations, we see that 1/a = 1/(t + 64) and 1/b = 1/(t + 25). Substituting these into the first equation, we have: t(1/(t + 64)) + t(1/(t + 25)) = 1 Multiplying both sides by (t + 64)(t + 25), we have: t(t + 25) + t(t + 64) = (t + 64)(t + 25) t^2 + 25t + t^2 + 64t = t^2 + 25t + 64t + 1600 t^2 = 1600 t = ±40 Since t can’t be negative, t = 40. Therefore, a = 40 + 64 = 104 and b = 40 + 25 = 65. So the ratio of the time taken by machine A to the time taken by machine B to complete this work is 104:65 = 8:5. Answer: B

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