GMATPASSION wrote:
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
\({\rm{times}}\,\,{\rm{A,}}\,B\,\,\,\,\,\, \to \,\,\,\,\,\min\)
\(? = {A \over B}\)
\(\left( * \right)\,\,\,\left\{ \matrix{
A = t + 64 \hfill \cr
B = t + 25 \hfill \cr} \right.\)
\({1 \over A} + {1 \over B} = {1 \over t}\,\,\,\,\left( {{\rm{stem}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{{1 \cdot B} \over {A \cdot B}} + {{1 \cdot A} \over {B \cdot A}} = {1 \over t}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{{2t + 89} \over {\left( {t + 64} \right)\left( {t + 25} \right)}} = {1 \over t}\)
\(2{t^2} + 89t = {t^2} + 89t + 25 \cdot 64\,\,\,\,\,\,\mathop \Rightarrow \limits^{t\,\, > \,\,0} \,\,\,\,\,t = 5 \cdot 8 = 40\)
\(?\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,{{40 + 64} \over {40 + 25}}\,\, = \,\,{{104:13} \over {65:13}} = {8 \over 5}\)
We follow the notations and rationale taught in the
GMATH method.
Regards,
Fabio.
_________________
Fabio Skilnik ::
GMATH method creator (Math for the GMAT)
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