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

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A plane traveled k miles in its first 96 minutes of flight time.  [#permalink]

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New post 26 Jan 2017, 05:37
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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
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Re: A plane traveled k miles in its first 96 minutes of flight time.  [#permalink]

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New post 26 Jan 2017, 05:48
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arslanama wrote:
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


total distance covered = K+300 miles
total time taken = 96+t minutes or (96+t)/60 hrs

avg speed = total distance / total time
= (k+300) / {(96+t)/60 } miles/hr
=60 ( k + 300 )/96 + t

Ans A
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Re: A plane traveled k miles in its first 96 minutes of flight time.  [#permalink]

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New post 26 Jan 2017, 09:22
arslanama wrote:
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


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Re: A plane traveled k miles in its first 96 minutes of flight time.  [#permalink]

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New post 30 Jan 2017, 16:56
1
arslanama wrote:
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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Re: A plane traveled k miles in its first 96 minutes of flight time.  [#permalink]

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New post 12 Sep 2018, 13:56
arslanama wrote:
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.
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Re: A plane traveled k miles in its first 96 minutes of flight time. &nbs [#permalink] 12 Sep 2018, 13:56
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