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# A plane traveled k miles in its first 96 minutes of flight

tagged by: AAPL

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## Global Stats

Difficult

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.

### GMAT/MBA Expert

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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.

_________________
Fabio Skilnik :: www.GMATH.net (Math for the GMAT)
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### GMAT/MBA Expert

GMAT Instructor
Joined
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Posted:
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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
We are given that a plane traveled k miles in 96 minutes. Since we need the average speed in miles per hour we can convert 96 minutes to hours.

96 minutes = 96/60 = 8/5 hours

We are also given that the plane completed the remaining 300 miles in t minutes. We must also convert t minutes to hours.

t minutes = t/60 hours

Now we can calculate the average speed for the entire trip, using the formula for average speed.

Average speed = total distance/total time

Average speed = (k + 300)/(8/5 + t/60) = (k + 300)/(96/60+t/60)

Average speed = (k + 300)/((96 + t)/60)

Average speed = 60(k + 300)/(96 + t)

_________________
Scott Woodbury-Stewart Founder and CEO

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