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It is 185 miles from Binghamton to New York City. If a bus takes 2 hou

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It is 185 miles from Binghamton to New York City. If a bus takes 2 hou [#permalink]

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New post 22 Oct 2017, 08:04
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It is 185 miles from Binghamton to New York City. If a bus takes 2 hours to travel the first 85 miles, how long must the bus take to travel the final 100 miles in order to average 50 miles an hour for the entire trip?

(A) 60 min
(B) 75 min
(C) 94 min
(D) 102 min
(E) 112 min
Spoiler: OA

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It is 185 miles from Binghamton to New York City. If a bus takes 2 hou [#permalink]

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New post 22 Oct 2017, 08:09
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Bunuel wrote:
It is 185 miles from Binghamton to New York City. If a bus takes 2 hours to travel the first 85 miles, how long must the bus take to travel the final 100 miles in order to average 50 miles an hour for the entire trip?

(A) 60 min
(B) 75 min
(C) 94 min
(D) 102 min
(E) 112 min


Total time for the trip \(= \frac{185}{50}\)

So time taken to travel \(100\) miles \(= \frac{185}{50}-2=\frac{85}{50} = 102\) min

Option D
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It is 185 miles from Binghamton to New York City. If a bus takes 2 hou [#permalink]

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New post 22 Oct 2017, 08:49
Bunuel wrote:
It is 185 miles from Binghamton to New York City. If a bus takes 2 hours to travel the first 85 miles, how long must the bus take to travel the final 100 miles in order to average 50 miles an hour for the entire trip?

(A) 60 min
(B) 75 min
(C) 94 min
(D) 102 min
(E) 112 min

Average speed = \(\frac{TotalDistance}{TotalTime}\)

AND (just rearranging)

Total time = \(\frac{TotalDistance}{Average
Speed}\)

In miles per hour, then, the total time it would take to average 50 miles per hour:

\(\frac{185}{50}\) = 3.7 hours

The bus has already traveled for 2 hours. Subtract that, and do not worry about the rate for those 2 hours. Rate for both legs has been accounted for in the "time taken" equation.

(3.7 - 2) = 1.7 hours still left to travel

Multiply any fraction of an hour by 60 to get minutes.

Minutes still remaining to travel the last leg (100 miles) of the trip:

1.7 hrs * 60 = 102 minutes, OR

\(1\frac{7}{10} = \frac{17}{10}hrs * \frac{60min}{1hr} = (17 * 6)mins\) =

102 minutes

Answer D
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It is 185 miles from Binghamton to New York City. If a bus takes 2 hou [#permalink]

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New post 22 Oct 2017, 09:00
Avg Speed = Total distance/Total time
50 = 185 / (t1 +t2) ---------------> t1 = 2hrs and t2 is what we have to find
50 = 185 / (2+t2)
100 + 50t2 =185
50t2 = 185 -100
t2 = 85/50 = 17/10 hrs
options in minutes --> multiply by 60
t2 = (17*60 )/10 = 102 mins- option D
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Re: It is 185 miles from Binghamton to New York City. If a bus takes 2 hou [#permalink]

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New post 22 Oct 2017, 22:19
Bunuel wrote:
It is 185 miles from Binghamton to New York City. If a bus takes 2 hours to travel the first 85 miles, how long must the bus take to travel the final 100 miles in order to average 50 miles an hour for the entire trip?

(A) 60 min
(B) 75 min
(C) 94 min
(D) 102 min
(E) 112 min


Time taken to travel 185 miles if 50 miles is average speed of trip = distance / speed = 185/50 = 3 hours 42 mins

Bus has covered 85 miles in first 2 hours .
Therefore , time remaining = 3 hours 42 mins - 2 hours = 1 hour 42 mins = 102 mins

Answer D
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Re: It is 185 miles from Binghamton to New York City. If a bus takes 2 hou   [#permalink] 22 Oct 2017, 22:19
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