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A car averages 55 mph for the first 4 hours of a trip and averages 70

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A car averages 55 mph for the first 4 hours of a trip and averages 70 [#permalink]

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New post 02 Nov 2015, 08:51
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A car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?

A. 6
B. 8
C. 11
D. 12
E. 14
[Reveal] Spoiler: OA

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Re: A car averages 55 mph for the first 4 hours of a trip and averages 70 [#permalink]

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New post 02 Nov 2015, 09:04
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Let the time for which car averages 70 mph = t

60*(t+4)= 55*4 + 70 t
=>10 t= 20
=> t = 2

Total duration of the trip = 4+2=6

Answer A
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Re: A car averages 55 mph for the first 4 hours of a trip and averages 70 [#permalink]

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New post 02 Nov 2015, 09:44
(4*55) + 70x / x + 4 = 60
220 + 70x = 60x + 240
10x = 20
x = 2

4 initial hours + 2 hours = 6 hours

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Re: A car averages 55 mph for the first 4 hours of a trip and averages 70 [#permalink]

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New post 23 Nov 2015, 00:29
Let x be the distance travelled at the speed of 70 mph

(4*55+70*x)/4+x=60
220+70x=240+60x
10x=20
x=2

Total distance =4+2=6

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Re: A car averages 55 mph for the first 4 hours of a trip and averages 70 [#permalink]

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New post 23 Nov 2015, 09:02
Bunuel wrote:
A car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?

A. 6
B. 8
C. 11
D. 12
E. 14


Distance travelled by the car in the first 4 hours is 55*4 = 220 miles

Let the time the car travelled after the first 4 hours be "t"

The total distance covered by the car in " t + 4 " hours is 220 + 70t = 60 ( t + 4)

Or, 220 + 70t = 60t + 240
Or, 10t = 20
Or, t = 2

So the time travelled by the car after the initial 4 hour is 2 hours.


Total time taken by the car is 4 + 2 = 6 Hours.
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Re: A car averages 55 mph for the first 4 hours of a trip and averages 70 [#permalink]

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New post 02 Dec 2015, 07:10
We can use the weighted average approach here, and we know we want total time. Which is just T= T1 + T2

Since we are given average rate at 60mph, which indicates that T1 is larger than T2, since R1 is only 5 away from the average, while R2 is 10 away.

T1=4 hours
R1 = 55 mph
T2=?
R2= 70 mph


(T1*R1 + T2*R2)/(T1+T2) = Tavg

Which is:
T1*R1 + T2*R2= T1*Tavg + T2*Tavg

T1*R1 - T1*Tavg = T2*avg - T2*R2

T1*(R1 - Tavg)= T2*(Tavg - R2)

T1/T2 = (Tavg - R2) / (R1 - Tavg)

Plugging in Values

4/T2 = (60-70) / (55 - 60)

4/T2 = -10 / - 5

4/T2 = 2

T2=2

T = T1 + T2
T = 4 + 2
T = 6

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Re: A car averages 55 mph for the first 4 hours of a trip and averages 70 [#permalink]

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New post 02 Dec 2015, 07:21
Bunuel wrote:
A car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?

A. 6
B. 8
C. 11
D. 12
E. 14


Distance travelled in first 4 hours = 55*4 = 220 miles

Let, remaining Time = t

i.e. Remaining Distance = 70*t

Total Distance = 60*(4+t)

i.e. 60*(4+t) = 220+70t

i.e. 240+60t = 220+70t
i.e. t = 2

i.e. Total Distance = 60*(4+t) = 60*(4+2) = 360
Total Time = 4+2 = 6 hours

Answer: option A
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Re: A car averages 55 mph for the first 4 hours of a trip and averages 70 [#permalink]

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A car averages 55 mph for the first 4 hours of a trip and averages 70 [#permalink]

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New post 05 Aug 2017, 00:58
by deduction (without using calculation), we should be able to establish that the number will be closer to the 4hr++ mark as avg speed of both was 60mph (ie closer to 55mph than 70mph) - 6hrs to be the most "reasonable" option.

please correct me if this is not reasonable.

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Re: A car averages 55 mph for the first 4 hours of a trip and averages 70 [#permalink]

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New post 09 Aug 2017, 12:50
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Bunuel wrote:
A car averages 55 mph for the first 4 hours of a trip and averages 70 mph for each additional hour. The average speed for the entire trip was 60 mph. How many hours long is the trip?

A. 6
B. 8
C. 11
D. 12
E. 14


We can let the time for the remainder of the trip = t, and thus:

average speed = (distance 1 + distance 2)/(time 1 + time 2)

60 = (55 x 4 + 70t)/(4 + t)

60(4 + t) = 220 + 70t

240 + 60t = 220 + 70t

20 = 10t

t = 2

Thus, the trip was 4 + 2 = 6 hours.

Answer: A
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Re: A car averages 55 mph for the first 4 hours of a trip and averages 70   [#permalink] 09 Aug 2017, 12:50
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