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On his trip from Alba to Benton, Julio drove the first x [#permalink]
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20 Dec 2005, 07:57
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On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first X miles? (1) On this trip, Julio drove for a total of 10 hours and a total of 530 miles (2) On this trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance How do you guys calculate for how many miles he drove 50 miles/hour and for how many miles he drove 60 miles an hour?
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Last edited by NoHalfMeasures on 15 Jan 2016, 07:58, edited 3 times in total.
Edited the question stem. Thanks to dimitri92.



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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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20 Dec 2005, 08:43
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He travels:
x*50 + y*60= kilometers, whereas x and y are respective times.
statement a gives us that the time x+y= 10 hours and the kilometers are 530, thus we have to equations and two variables.
x*50 + y*60=530
x + y = 10 or y = 10  x



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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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20 Dec 2005, 09:55
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sandalphon wrote: On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 milesper hour. How long did it take Julio to drive the first x miles?
(a) On this trip, Julio drove for a total of 10 hours and drove a total of 530 miles.
How do you guys calculate for how many miles he drove 50 miles/hour and for ho wmany miles he drove 60 miles an hour?
I'm assuming this is a PS question...
rt=D
I would set it up like this; we will call the 2 segments of the trip A, and B.
....... A ........ B R ..... 50 ...... 60
T ...... t ....... 10t
D ....... x ....... 530x
Derive 2 equations from this.
50t = x
60(10t) = 530x
Substitute
600  60t = 530  50t
Solve for t, you get t = 7... Answer is 7 hours



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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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20 Dec 2005, 14:27
7 HOURS
SIMPLIFIED...............
total time =10 h
total distance 530 miles
average speed different,
for x mile, 50m/h, and for (530x) miles 60m/h
from this x/50 h+ (530x)/60 h =10 h
so x=350 miles
and 350miles/50m/h = 7h



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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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20 Dec 2005, 19:09
d = rt
x = 50t < eq1
530  x = 60(10  t)
530  x = 600  60t < substitute 50t for x
you will get t = 7



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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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20 Dec 2005, 19:17
If he travelled x miles at 50miles per hour and the remaining distance at 60 miles per hour, then this remaining distance is (530x)miles.
You can calculate x by equating:
x/50 + (530x)/60 = 10



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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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08 Jun 2010, 09:07
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sandalphon wrote: On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 milesper hour. How long did it take Julio to drive the first x miles?
(a) On this trip, Julio drove for a total of 10 hours and drove a total of 530 miles.
How do you guys calculate for how many miles he drove 50 miles/hour and for ho wmany miles he drove 60 miles an hour? the complete question is.. On his trip from Alba to Benton, Julia drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first x miles ? 1) On his trip, Julio drove for a total of 10 hrs and drove a total of 530 miles 2) On his trip,it took Julio 4 more hours to drive the first x miles than to drive the remaining distance. Solution: d=vt
let d=total distance t1=total time taken to cover x miles t2=total time taken to cover dx miles (the remaining miles)
t1=x/50 ; t2=(dx)/60 > we have these equations before even looking at the statemenets
statement(1) t1+t2=10; d=530 put the values in the above equations
x/50 + (530x)/60 = 10
no need to calculate x's value. just looking at the equation, we can see that x's value can be determined and, thus, the value of t1 can be determined.
SUFFICIENT
statement(2) t1=t2+4 we still don't know the value of d, so we can't calculate the value of t1.
INSUFFICIENT
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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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15 May 2011, 18:29
Can somebody answer this 
What is wrong with using smart numbers to solve the 2
assume distance is 300
50 * (t+4) = x 60 * (t) = 300x
Add it up
50*(t+4) + 60*(t) = 300
And solve for t



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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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15 May 2011, 19:37
Lets solve this by alligation. From Statment 1: Avg speed=53 mile/hr it comes from avg of 2 speeds 50 and 60 (as per Q) 505360 53 is closer to 50 hence we need travel more at 50 miles/hr speed. Total hours 10 need to divided in to speeds 50 and 60. Time spend will be in inverse ration of two speeds 505360 7hrs3 hrs @shantascherla: how can you assume numbers when they are given in the question. Well but i think it will work if you are solving DS question and you are aware that you dont need to find the correct answer. All you got to do is find out if a Unique ans is possible or not.
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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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15 May 2011, 20:01
shantascherla wrote: Can somebody answer this 
What is wrong with using smart numbers to solve the 2
assume distance is 300
50 * (t+4) = x 60 * (t) = 300x
Add it up
50*(t+4) + 60*(t) = 300
And solve for t clean A here. 2 X = (t+4) * 50 DX = t * 60 Assuming D will clearly give you t here and hence X. However, this is not given in the question stem. Hence to be avoided.
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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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16 May 2011, 05:03
(1) x/50 + (530x)/60 = 10 Sufficient (2) x/50 = y/60 + 4 Not Sufficient Answer  A
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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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18 Jul 2011, 23:38
SunShine wrote: 7 HOURS
SIMPLIFIED...............
total time =10 h
total distance 530 miles
average speed different,
for x mile, 50m/h, and for (530x) miles 60m/h
from this x/50 h+ (530x)/60 h =10 h so x=350 miles and 350miles/50m/h = 7h How do you get x = 350? Isnt x = 35 instead of 350 ?? because at the end if you solve the equation you get x = 350/10 ...see below x/50 + (530  x)/60 = 10 10x/300 = 10  (530/60) 10x/300 = 600530/60 10x/300 = 7/6 x = (7 *300) / (10*6) = 35 ???



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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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22 Nov 2016, 07:50
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sandalphon wrote: On his trip from Alba to Benton, Julio drove the first x miles at an average rate of 50 miles per hour and the remaining distance at an average rate of 60 miles per hour. How long did it take Julio to drive the first X miles?
(1) On this trip, Julio drove for a total of 10 hours and a total of 530 miles (2) On this trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance
How do you guys calculate for how many miles he drove 50 miles/hour and for how many miles he drove 60 miles an hour? the answer is A. i created two expressions time traveled first x miles: x/50 time traveled remaining part: Dx/60, where D is the total distance. 1. D = 530, and we can write: x/50 + 530x/60 = 10 > we can solve for X, we can find x/50  sufficient. 2. x/50  Dx/60 = 4 > we still have 2 unknowns, we can't answer the question  not sufficient.



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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]
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29 Sep 2017, 20:33
I did this by creating an R*T = D table and separated the two trips
Let d be distance in part A of the trip Let t be the time in part A of the trip
Let D be total distance Let T be total time
Rate * Time = Distance Trip A 50 * t = d Trip B 60 * Tt = Dd
By looking at this, you have 4 variables and 2 equations.
Statement 1: T = 10 D = 530 This reduces to 2 variables and 2 equations. Sufficient
Statement 2: t+4 this only tells us the rough difference. It could be t=8, making T=12 or t=10, making T=14 Insufficient




Re: On his trip from Alba to Benton, Julio drove the first x
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