Problem Solving

Veritas Prep

A plane traveled k miles in its first 96 minutes of flight time. If it completed the remaining 300 miles of the trip in t minutes, what was its average speed, in miles per hour, for the entire trip?

A. 60 ( k + 300 )/96 + t
B. kt + 96 ( 300 ) / 96t
C. k + 300 / 60 ( 96 + y )
D. (5k / 8) + (60(300) / t)
E. (5k / 8) + 5t

OA A.

AAPL wrote:Veritas Prep

A plane traveled k miles in its first 96 minutes of flight time. If it completed the remaining 300 miles of the trip in t minutes, what was its average speed, in miles per hour, for the entire trip?

A. 60 ( k + 300 )/(96 + t)
B. kt + 96 ( 300 ) / 96t
C. k + 300 / 60 ( 96 + y )
D. (5k / 8) + (60(300) / t)
E. (5k / 8) + 5t

Simple application of UNITS CONTROL, one of the most powerful tools of our method!

\[? = \frac{{\left[ {{\text{total}}\,\,\# \,\,{\text{miles}}} \right]}}{{\left[ {{\text{total}}\,\,\# \,\,\min } \right]}}\,\,\frac{{{\text{miles}}}}{{\min }}\,\,\,\left( {\frac{{60\,\,\min }}{{1\,\,\,{\text{h}}}}\,\,\begin{array}{*{20}{c}}
\nearrow \\
\nearrow
\end{array}} \right)\,\,\, = \,\,60 \cdot \left( {\frac{{\left[ {{\text{total}}\,\,\# \,\,{\text{miles}}} \right]}}{{\left[ {{\text{total}}\,\,\# \,\,\min } \right]}}} \right)\,\,\,{\text{mph}}\,\,\,\]
(Arrows indicate licit converter.)

\[\left[ {{\text{total}}\,\,\# \,\,{\text{miles}}} \right] = k + 300\]
\[\left[ {{\text{total}}\,\,\# \,\,\min } \right]\,\,{\text{ = }}\,\,96 + t\]

\[? = \frac{{60\,\left( {k + 300} \right)}}{{96 + t}}\]

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

Regards,
Fabio.