Problem Solving

EMPOWERgmat

An assembly line produces 40 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the average output, in cogs per hour, for the assembly line during this time?

A. 42
B. 45
C. 48
D. 50
E. 55

OA C

AAPL wrote:EMPOWERgmat

An assembly line produces 40 cogs per hour until an initial order of 60 cogs is completed. The speed of the assembly line is then immediately increased so that it can produce 60 cogs per hour until another 60 cogs are produced. What is the average output, in cogs per hour, for the assembly line during this time?

A. 42
B. 45
C. 48
D. 50
E. 55

$$? = {{\# \,\,{\rm{cogs}}} \over {\# \,\,{\rm{hours}}}}$$
Trivial application of UNITS CONTROL, one of the most powerful tools of our method!

$${V_1} = {{40\,\,{\rm{cogs}}} \over {{\rm{1}}\,\,{\rm{h}}}}\,\,\,{\rm{for}}\,\,\,60\,\,{\rm{cogs}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{T_1}\,\,\, = \,\,\,60\,\,{\rm{cogs}}\,\,\,\left( {{{1\,\,{\rm{h}}} \over {40\,\,cogs}}} \right)\,\,\, = \,\,\,{3 \over 2}\,\,{\rm{h}}$$
$${V_2} = {{60\,\,{\rm{cogs}}} \over {{\rm{1}}\,\,{\rm{h}}}}\,\,\,{\rm{for}}\,\,\,\left( {{\rm{extra}}} \right)\,\,60\,\,{\rm{cogs}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{T_2}\,\,\, = \,\,\,60\,\,{\rm{cogs}}\,\,\,\left( {{{1\,\,{\rm{h}}} \over {60\,\,cogs}}} \right)\,\,\, = \,\,\,1\,\,{\rm{h}}$$

$${\rm{?}}\,\,\,\,{\rm{ = }}\,\,\,\,{{60 + 60} \over {{3 \over 2} + 1}}\,\,\,\, = \,\,\,\,{{2 \cdot 120} \over 5}\,\,\,\, = \,\,\,\,48\,\,\,\left[ {{{{\rm{cogs}}} \over {\rm{h}}}} \right]$$

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

Regards,
Fabio.