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

Question

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.

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?

Bunuel · Accepted Answer

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.

allabout · Answer

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

yb · Answer

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

dimitri92 · Answer

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

MICKEYXITIN · Answer

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?

Bunuel · Answer

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 .

MICKEYXITIN · Answer

thanks Bunuel, how foolish i am

ankitranjan · Answer

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).

mvictor · Answer

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.

SchruteDwight · Answer

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

Basshead · Answer

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.

sanjeevsinha082 · Answer

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

Crytiocanalyst · Answer

(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

Kimberly77 · Answer

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

BrentGMATPrepNow · Answer

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.

totaltestprepNick · Answer

A https://www.youtube.com/watch?v=mDEsV2LgSgw Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

Usernamevisible · Answer

Bunuel   KarishmaB  - for statement 2, why it is not sufficient ?

speed ratio is 5:6 so time is 6:5 which means 1 part per statement B is 4 hours thus first part time taken becomes 6*4=24 hours ?

Thus B alone is also sufficient giving answer as D

Maybe I got the reason so editing the post -

You cannot use inverse speed ratio (time ratio = 6:5) unless the distances are equal.
Why your approach breaks:
You assumed:
 t1 : t2 = 6 : 5
But in reality:
 t1 = x / 50
 t2 = (total − x) / 60
So:
 t1 : t2 = (x / 50) : ((total − x) / 60)
This ratio depends on x. It is not fixed.
What you unintentionally did:
By setting:
 t1 = 6k and t2 = 5k
You forced:
 (x / 50) : ((total − x) / 60) = 6 : 5
Solving this leads to:
 x = total − x
 x = total / 2
Meaning:
 first distance = second distance
But this condition is NOT given in the question. You added it implicitly.
Why Statement (2) is not sufficient:
Given:
 t1 = t2 + 4
This is only one equation with multiple unknowns.
Check two valid cases:
Case 1:
 t2 = 2, t1 = 6
 Distances: 120 and 300
Case 2:
 t2 = 20, t1 = 24
 Distances: 1200 and 1200
Both satisfy the condition (difference = 4), but t1 is different.
Therefore, multiple answers exist → not sufficient.
Final rule:
Inverse speed ratio gives time ratio only when distances are equal.

Bunuel · Answer

Your ratio step is the mistake. Time is in the inverse ratio of speeds only when the two distances are the same, but here the first part and the remaining part are not given to be equal.

KarishmaB · Answer

Your updated Final Rule is correct. Check this out too:   https://youtu.be/7ASEIvxYPCM

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

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