Problem Solving

AAPL wrote:Princeton Review

Jake and Ryan worked together on a job for which they were each paid a dollars in advance. If Jake spent 20% more time working on the job than Ryan did, and Ryan gave Jake b dollars, so that their hourly wages were equal, then, in terms of b, how much was Jake paid in advance?

A. 0.8b
B. 1.1b
C. 1.2b
D. 10b
E. 11b

$$\left. \matrix{
{\rm{Ryan}}\,\,\left\{ \matrix{
\,\,5t\,\,\,{\rm{hours}} \hfill \cr
\,\,\$ \,\,\left( {a - b} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{{a - b} \over {5t}}\,\,\,{\$ \over {{\rm{hour}}}} \hfill \cr
{\rm{Jake}}\,\,\,\,\left\{ \matrix{
\,\,5t + {1 \over 5}\left( {5t} \right) = 6t\,\,\,{\rm{hours}} \hfill \cr
\,\,\$ \,\,\left( {a + b} \right) \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,{{a + b} \over {6t}}\,\,\,{\$ \over {{\rm{hour}}}}\,\,\,\,\,\, \hfill \cr} \right\}\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{stem}}} \,\,\,\,\,\,\,\,{{a - b} \over {5t}} = \,\,\,\,{{a + b} \over {6t}}$$
$$?\,\,:\,\,\,a = f\left( b \right)$$
$${{a - b} \over {5t}} = \,\,\,\,{{a + b} \over {6t}}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,6\left( {a - b} \right) = 5\left( {a + b} \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,?\,\,\,:\,\,\,a = 11b$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.