Problem Solving

Veritas Prep

When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 44 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?

A. 5 minutes, 17.6 seconds
B. 5 minutes, 21.8 seconds
C. 5 minutes, 43.56 seconds
D. 5 minutes, 44.44 seconds
E. 6 minutes, 10.4 seconds

OA E

AAPL wrote:Veritas Prep

When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 44 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?

A. 5 minutes, 17.6 seconds
B. 5 minutes, 21.8 seconds
C. 5 minutes, 43.56 seconds
D. 5 minutes, 44.44 seconds
E. 6 minutes, 10.4 seconds

Good problem!
\[? = 5\min 44{\text{s}} + \frac{{11}}{{25}}\min \]

\[\frac{{11}}{{25}}\min \,\,\left( {\frac{{60{\text{s}}}}{{1\min }}} \right)\,\,\, = \,\,\,\frac{{11 \cdot 12}}{5}{\text{s}}\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,26\frac{2}{5}{\text{s}}\]

\[\left( * \right)\,\,\,\frac{{\left( {10 + 1} \right) \cdot 12}}{5} = \underleftrightarrow {2 \cdot 12 + \frac{{12}}{5} = 24 + \frac{{10 + 2}}{5}} = 26\frac{2}{5}{\text{s}}\]

\[? = 5\min 44s + 16s + 10s + \frac{2}{5}s = 6\min 10.4\,{\text{s}}\]

The above follows the notations and rationale taught in the GMATH method.

POST-MORTEM: the alternative choices help you avoid the precise calculations above, BUT I think they are very instructive...

A first way to solve it:
The stopwatch starts to work after Nuria began her running. It means the time should be greater than credited 5 minutes, 44 seconds.
The only number is 6 minutes, 10.4 seconds.

A second way to solve it:
11/25 close to 30 seconds when added to the 5 minutes, 44 seconds, it means passes 6 minutes.

Regards.