On his trip from Alba to Benton, Julio drove the first x miles at an

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 --> \(total \ time=10=\frac{x}{50}+\frac{530-x}{60}\) --> we have the linear equation with one unknown, so we can solve for \(x\). Sufficient.

(2) On this trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance --> \(\frac{x}{50}=\frac{y}{60}+4\), where \(y\) is the remaining distance --> we have the linear equation with two unknowns, so we cannot solve for \(x\). Not sufficient.

Answer: A.
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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

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

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

i've got sufficient with (1)
However with (2), we are told that : "it took Julio 4 more hours to drive the first x miles than to drive the remaining distance " can we have the fomular as folow:
r1 = 50m/h
r2 = 60m/h
1 hour: we have the difference miles between the first x mile and the remaining = 10m
=> with 4 hours: we can find the distance of the remaining distance = x + (10m/h x 4h) = x + 40miles
=> we have the equation with one unknown as we have solved the remaining distance.
Please tell me where i did get the wrong refers?

Remaining distance, \(y\), won't be \(x+40\). If \(t\) is the time to cover \(y\) then the time to cover \(x\) will be \(t+4\) then \(x=(t+4)*50=50t+200\).
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thanks Bunuel, how foolish i am

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 drove 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.


From the statement :

If the total distance is D.

(x/50) + + (D-x)/60 = Total Time

Now from (1), (x/50) + + (D-x)/60 =10
and D = 530
From the above two equation x can be calculated and so x/50. Hence sufficient

From (2), x/50 + 4 = (D-x)/50
One equation and two unknown ,Hence impossible to find out x. ( Not sufficient)


Therefore answer in (A).

the answer is A.
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.

I think a lot of people are thinking too hard with this one.

If we are given both the total time and the total speed, we can calculate the average rate as \(\frac{530}{10}=53\) From thereon, it becomes a mixture problem. 53 means that the rates of 50 and 60 were mixed in the ratio 7:3, and therefore the total time driven at each of these rates is 3:7 (as time is the inverse of speed).

Absolutely no reason to do any time-consuming calculations. Always try higher-level thinking first
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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 drove a total of 530 miles.

Lets think about what this statement is telling us. If Julio drove 10 hours at a rate of 60 miles per hour, Julio would have drove 600 miles. If Julio drove 10 miles at 50 miles per hour, Julio drove 500 miles. We are told Julio drove for a total of 10 hours and 530 miles. 530 is weighted more heavily towards 50 with a ratio of 7 : 3. Therefore, Julio drove 7 hours at a rate of 50 miles per hours. Sufficient.

(2) On this trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance.

We don't know the total distance. Insufficient.

Answer is A.
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1). x/50+(530-x)/60=10, so, x can be solve out and x/50 will be the answer
2). The time cost on two distances could be 5h, 1h; 6h, 2h;... insufficient.
Answer is A

(1) On this trip, Julio drove for a total of 10 hours and drove a total of 530 miles.
let the time taken in x miles be t then x/t=50 ; 530-x/10-t=60
=>2 eqns and 2 variable we can definitely get t
Clearly suff

(2) On this trip, it took Julio 4 more hours to drive the first x miles than to drive the remaining distance.
t1=50/x;t2=60/y-x where y is the total distance
since this is 2 eqn and 3 variable we cannot solve for the variables without another equation therefore
IMO A

Hi BrentGMATPrepNow, for St2, can we not assume second x miles as 100 - x here? Therefore is sufficient?
x/50 = 4 + (100-x)/60

Where did you get 100 miles as the total distance?
There's nothing in the question that suggests the total distance from Alba to Benton is 100 miles.