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

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

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

by AAPL » Wed Sep 12, 2018 5:28 am

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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.

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Source: Beat The GMAT — Problem Solving | Wed Sep 12, 2018 5:28 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Wed Sep 12, 2018 1:51 pm

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 :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Sep 14, 2018 8:25 am

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)

Answer: A

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