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

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Manager
Joined: 05 Nov 2005
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On his trip from Alba to Benton, Julio drove the first x [#permalink]

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Updated on: 15 Jan 2016, 08:58
1
11
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Difficulty:

55% (hard)

Question Stats:

63% (01:28) correct 37% (01:24) wrong based on 368 sessions

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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?

Originally posted by sandalphon on 20 Dec 2005, 08:57.
Last edited by NoHalfMeasures on 15 Jan 2016, 08:58, 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, 09:43
2
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, 10:55
1
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 ....... 10-t

D ....... x ....... 530-x

Derive 2 equations from this.

50t = x
60(10-t) = 530-x

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, 15:27
7 HOURS

SIMPLIFIED...............

total time =10 h

total distance 530 miles

average speed different,

for x mile, 50m/h, and for (530-x) miles 60m/h

from this x/50 h+ (530-x)/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, 20:09
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, 20:17
If he travelled x miles at 50miles per hour and the remaining distance at 60 miles per hour, then this remaining distance is (530-x)miles.

You can calculate x by equating:

x/50 + (530-x)/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, 10:07
1
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 d-x miles (the remaining miles)

t1=x/50 ; t2=(d-x)/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 + (530-x)/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, 19:29

What is wrong with using smart numbers to solve the 2

assume distance is 300

50 * (t+4) = x
60 * (t) = 300-x

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, 20:37
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)
50--53------60
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
50--53------60
7hrs--------3 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, 21:01
shantascherla wrote:

What is wrong with using smart numbers to solve the 2

assume distance is 300

50 * (t+4) = x
60 * (t) = 300-x

50*(t+4) + 60*(t) = 300

And solve for t

clean A here.

2- X = (t+4) * 50 D-X = 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, 06:03
(1)

x/50 + (530-x)/60 = 10

Sufficient

(2)

x/50 = y/60 + 4

Not Sufficient

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Joined: 29 Jan 2011
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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]

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19 Jul 2011, 00:38
SunShine wrote:
7 HOURS

SIMPLIFIED...............

total time =10 h

total distance 530 miles

average speed different,

for x mile, 50m/h, and for (530-x) miles 60m/h

from this x/50 h+ (530-x)/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 = 600-530/60

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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22 Nov 2016, 08:50
1
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?

i created two expressions
time traveled first x miles: x/50
time traveled remaining part: D-x/60, where D is the total distance.

1. D = 530, and we can write:
x/50 + 530-x/60 = 10 -> we can solve for X, we can find x/50 - sufficient.

2. x/50 - D-x/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, 21:33
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 * T-t = D-d

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
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Re: On his trip from Alba to Benton, Julio drove the first x [#permalink]

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18 Apr 2018, 03:12
Hi Bunuel VeritasPrepKarishma

Can you help me for option B

If we know Speed for 1st half 1/Speed for second half 2 = 50/60 (5/6), then t1/t2 = 6/5 (speed is inversely proportional)
Now from 2 we know t1 = t+4 & t2 = t so t1/t2 = t+4/t = 6/5 from prev eqn.. cant we solve it then ??
Re: On his trip from Alba to Benton, Julio drove the first x   [#permalink] 18 Apr 2018, 03:12
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