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# A car averages 40 miles per hour for the first 6 hours of a

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Senior Manager
Joined: 20 Feb 2007
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A car averages 40 miles per hour for the first 6 hours of a [#permalink]

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14 Mar 2007, 03:05
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Difficulty:

55% (hard)

Question Stats:

61% (09:30) correct 39% (01:52) wrong based on 305 sessions

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A car averages 40 miles per hour for the first 6 hours of a trip and averages 60 miles per hour for each additional hour of travel time. If the average speed for the entire trip is 55 miles per hour, how many hours long is the trip?

A. 8
B. 12
C. 16
D. 18
E. 24
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Jun 2014, 14:19, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.

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Re: A car averages 40 miles per hour for the first 6 hours of a [#permalink]

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14 Mar 2007, 03:12
(40*6+60*x)/x+6=55
240+60x=55x+330
5x=90
x=18

6+18=24

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Senior Manager
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Re: A car averages 40 miles per hour for the first 6 hours of a [#permalink]

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14 Mar 2007, 03:22
Oh....I don't know how I could not see it!

Somehow I wrote it 240+60x=55+330 and got it all wrong.....

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Senior Manager
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Re: A car averages 40 miles per hour for the first 6 hours of a [#permalink]

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14 Mar 2007, 03:24
I realized now my mistakes are limited to some silly stuff, solving the Qs correctly but being careless to write all the equations properly.....I must be very vary careful

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Re: A car averages 40 miles per hour for the first 6 hours of a [#permalink]

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23 Jun 2014, 14:00
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Total distance = (40 * 6 + 60 + t)
Total time = (6 + t)
Solving Average speed = Total distance/Total time, for t,
t = 18
Total time = 18 + 6 = 24

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Re: A car averages 40 miles per hour for the first 6 hours of a [#permalink]

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23 Jun 2014, 16:41
total distance = rate * time

if total time taken is x, this equation can be written as
40(x-6) + 60(x) = 55x

48+12x-72 = 11x

x = 24

Ans: E

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Re: A car averages 40 miles per hour for the first 6 hours of a [#permalink]

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23 Jun 2014, 20:50
1
KUDOS
Refer diagram below:

Setting up the equation to find "t"

240 + 60(t-6) = 55t

t = 24

Attachments

dis.jpg [ 25.28 KiB | Viewed 2685 times ]

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Re: A car averages 40 miles per hour for the first 6 hours of a [#permalink]

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23 Jun 2014, 23:47
40x6 + 60xt = 55(6 + t)
t = 18
Total time = 18 + 6 = 24

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Re: A car averages 40 miles per hour for the first 6 hours of a [#permalink]

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07 Nov 2015, 12:04
for the first part, the car travels 240 miles
then the car makes 60miles per hour, and drives for X hours.

the average speed is 55 miles/h we need to find the total number of hours.

we can establish the equations:
distance driven after the first 240 miles is Rate*Time. Rate=60mph time = xh or 60x miles
total time traveled is 6h + x h
average velocity for the entire trip - 55 mph.
rewrite everything as:
240 + 60x = 55(6+x) or
240+60x = 330 + 55x - substract 55 x and 240
5x = 90
x = 18
this is not the final answer. D is a trap!!!
total time for the trip is 18+6 = 24.
thus, 24 hours. E.

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Re: A car averages 40 miles per hour for the first 6 hours of a   [#permalink] 07 Nov 2015, 12:04
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