On his trip from Alba to Bento, 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 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 hour to drive the first x miles than to drive the remaining distance.

As the OA was again not provided this is how I solved it. Can someone be please kind enough to let me know whether I am right or wrong?

Here is how I solved it:

Let's say:

Total Distance - D

Time required to travel x miles - T1

Time required to travel D-x miles - T2

Rate to travel x miles - 50mph

R=D/T => 50=x/T1 and therefore x = 50*T1 ----------------------------------------------(1)

R=D/T => 60=D-x/T2 and therefore x = D-60*T2 ------------------------------------------(2)

So now the question becomes what is T1?

Considering Statement 1T1+T2=10

T2=10-T1 -------------------------------------------------------------------------------(3)

D = 530

Substituting the value of D in equation 2 above

x = 530-60*T2

Considering the total distance is D, we can say Equation 1 is equal to Equation 2 i.e.

50*T1 = 530-60*T2 ----------------------------------------------------------------------(4)

Substituting the value of T2 from equation 3 to equation 4 will give me the value of T1 and therefore is sufficient to answer the question.

Considering Statement 2Speed to cover first x miles = 50 mph

Let T1 be the time required to cover x miles & D be the total distance

As R=D/T, we know x/T1+4=50 ------------------------(1)

x-D/T1= 60 ------------------------(2)

2 equations and 3 variables therefore insufficient.

Therefore, statement 1 alone is sufficient to answer this question.

_________________

Best Regards,

E.

MGMAT 1 --> 530

MGMAT 2--> 640

MGMAT 3 ---> 610

GMAT ==> 730