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On the first day of her vacation, Louisa traveled 216 miles.

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On the first day of her vacation, Louisa traveled 216 miles. [#permalink]

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New post 18 Dec 2010, 11:02
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On the first day of her vacation, Louisa traveled 216 miles. On the second day, traveling at the same average speed, she traveled 378 miles. If the 216-mile trip took 3 hours less than the 378-mile trip, what was the average speed, in miles per hour?

A. 31
B. 38
C. 50
D. 54
E. 56

Hey All,

This question is not difficult. I got the question correct rather quickly by using the Plug in method. I want to make sure I understand how to quickly solve this problem using algebra. Can someone please walk me through this. Thanks!
[Reveal] Spoiler: OA

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Re: ETS Paper test Rates problem. Need help with the Algebra [#permalink]

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New post 18 Dec 2010, 11:25
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tonebeeze wrote:
Hey All,

This question is not difficult. I got the question correct rather quickly by using the Plug in method. I want to make sure I understand how to quickly solve this problem using algebra. Can someone please walk me through this. Thanks!

"On the first day of her vacation, Louisa traveled 216 miles. On the second day, traveling at the same average speed, she traveled 378 miles. If the 216-mile trip took 3 hours less than the 378-mile trip, what was the average speed, in miles per hour?"

1. 31
b. 38
c. 50
d. 54
3. 56


(time)*(rate) = (distance) --> (rate) = (distance)/(time) --> given: (rate) = 216/t = 378/(t+3) --> 4/t = 7/(t+3) --> t=4 --> (rate) = 216/4 = 54.

Answer: D.

Hope it's clear.
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Re: ETS Paper test Rates problem. Need help with the Algebra [#permalink]

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New post 18 Dec 2010, 19:08
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tonebeeze wrote:
Hey All,

This question is not difficult. I got the question correct rather quickly by using the Plug in method. I want to make sure I understand how to quickly solve this problem using algebra. Can someone please walk me through this. Thanks!

"On the first day of her vacation, Louisa traveled 216 miles. On the second day, traveling at the same average speed, she traveled 378 miles. If the 216-mile trip took 3 hours less than the 378-mile trip, what was the average speed, in miles per hour?"

1. 31
b. 38
c. 50
d. 54
3. 56


Rather than plugging numbers, the easier way would be to use logic here...
216 mile trip took 3 hrs less because Louisa traveled 162 miles (= 378 - 216) less. That means her average speed must be 162/3 = 54 miles/hr.
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Re: On the first day of her vacation, Louisa traveled 216 miles. [#permalink]

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New post 11 Dec 2013, 10:49
let v be the speed of travel; let time be x and x-3; since the speed is the same you can do 216/x-3=778/x

you got x =7 and you can find the avg speed for the entire trip simply by doing 594(total distance)/(4+7)= 54 ans e

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Re: On the first day of her vacation, Louisa traveled 216 miles. [#permalink]

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New post 14 May 2014, 13:18
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Let, Speed be x
(378/x) –(216/x) = 3 , x= 54

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Re: On the first day of her vacation, Louisa traveled 216 miles. [#permalink]

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New post 21 May 2014, 07:55
Just to elaborate,

Lets take average speed of Louisa is v miles per hour

Total time taken on first day to travel 216 miles = 216/v

Total time taken on second day to travel 378 miles = 378/v

Travelling time on first day is 3 hour less than travelling time on second day

travel time on first day = travel time on second day -3

216/v = 378/v - 3

162/v = 3
or v = 162/3 = 54

Hence Answer is D
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Re: On the first day of her vacation, Louisa traveled 216 miles. [#permalink]

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New post 03 Nov 2017, 03:23
tonebeeze wrote:
On the first day of her vacation, Louisa traveled 216 miles. On the second day, traveling at the same average speed, she traveled 378 miles. If the 216-mile trip took 3 hours less than the 378-mile trip, what was the average speed, in miles per hour?

A. 31
B. 38
C. 50
D. 54
E. 56

Hey All,

This question is not difficult. I got the question correct rather quickly by using the Plug in method. I want to make sure I understand how to quickly solve this problem using algebra. Can someone please walk me through this. Thanks!


hi

378/x - 216/x = 3
or, x = 54

thanks

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Re: On the first day of her vacation, Louisa traveled 216 miles. [#permalink]

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New post 06 Nov 2017, 17:33
tonebeeze wrote:
On the first day of her vacation, Louisa traveled 216 miles. On the second day, traveling at the same average speed, she traveled 378 miles. If the 216-mile trip took 3 hours less than the 378-mile trip, what was the average speed, in miles per hour?

A. 31
B. 38
C. 50
D. 54
E. 56


We can let the time to travel the 216 miles = t and the time to travel the 378 miles = t + 3. Since the rates are the same and rate = distance/time, we have:

216/t = 378/(t + 3)

216(t + 3) = 378t

216t + 648 = 378t

648 = 162t

4 = t

Thus, the average speed was 216/4 = 54 mph.

Answer: D
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Re: On the first day of her vacation, Louisa traveled 216 miles.   [#permalink] 06 Nov 2017, 17:33
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On the first day of her vacation, Louisa traveled 216 miles.

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