ETS Paper Test Rates Problem. Need help with the Algebra

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tonebeeze: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Nov 02, 2009 5:49 pm; Thanked: 2 times; Followed by:3 members

ETS Paper Test Rates Problem. Need help with the Algebra

by tonebeeze » Sat Dec 18, 2010 10:09 am

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

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Source: Beat The GMAT — Problem Solving | Sat Dec 18, 2010 10:09 am

beat_gmat_09: Master | Next Rank: 500 Posts; Posts: 437; Joined: Sat Nov 22, 2008 5:06 am; Location: India; Thanked: 50 times; Followed by:1 members; GMAT Score:580

by beat_gmat_09 » Sat Dec 18, 2010 10:17 am

Let S = average speed for both the trips.
t = time taken for travelling 378 miles.

216/(t-3) = S ........ (1) ....... for 216 miles
378/t = S...............(2) .........for 378 miles.
equate (1) and (2) as speed is same
216/(t-3) = 378/t

= 72/(t-3) = 126/t
4/(t-3) = 7/t
4t = 7t - 21
3t = 21
t = 7

S = 378/7
S = 54 miles/hr

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N:Dure: Master | Next Rank: 500 Posts; Posts: 181; Joined: Sat Oct 16, 2010 1:57 pm; Thanked: 4 times

by N:Dure » Sat Dec 18, 2010 10:45 am

s= 216/t

s= 378 /t+3

216/t = 378/ t+3

72/t = 126 / t+3

72 t + 216 = 126 t

t= 4

s = 216/4 = 54

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Jan 09, 2018 9:59 am

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

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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