Maria drove a distance without stopping such that she covered first

How C is the correct answer. B is sufficient to solve

Hello Princ

Sorry for late reply. But as per my understanding, 'difference between x and y' could mean either x-y or y-x, we cant say what unless something else is also mentioned.

HI @Experts, Could you please provide a solution for this question?

Let's assume 'X' to be the total distance covered by both of them.
The question says that Maria covered X/3 in 4h and the remaining 2X/3 in 4h. Hence, the total time Tm = 7h and average speed Sm = X/7.
Next, Sarah covered X/3 with 60mph(in t1 time) and remaining 2X/3 with 40mph(in t2 time). So total time, T= t1+t2
=> {X/3}/60 + {2X/3}/40 = X/180 + X/60 = X/45.
(1) Statement 1 says Sarah covered X in lesser time than Maria. So x/45 < 7 => X < 315. NOT SUFFICIENT!

(2) Statement 2 says Ss - Sm = 10. Average speed = Total Distance, X/Total Time, T.
Ss = X/(X/45) => 45
Sm = X/7
Hence, 45 - X/7 = 10
315 - X = 70
X = 245.
SUFFICIENT!
ANSWER B?
Please correct me if I'm wrong

You are wrong here: (2) Statement 2 says Ss - Sm = 10.
Actually statement 2 says that |Ss - Sm| = 10
so it could be 10 or -10

The question says, Sarash covered first 1/3 of time in 60 m/h speed. This doesn't mean 1/3 of the total distance, but what it means is 1/3 of the total time that Sarah spent on the road she drove for 60 m/h and rest 2/3 time that she spent on road for 45 m/h. All the difficulty in this problem lies in this portion only.

Bunuel gmatbusters VeritasKarishma please can you help in this?

deddex,
Solution is as per sketch:

Hi prince

Difference between two numbers is always non negative.

Thanks for pointing out the typo in the book. It will be revised.

Regards


Posted from my mobile device

Maria:
distance =x
speed=m=x/7
time =7

Sarah
distance =x=60t + 45*2t=150t
speed=s=x/(3t) =50
time =3t

x=?

1, m<s
7> 3t --> 350>x
2, |s-m|=10
1+2, 50 - x/7 = 10 --> x=280


C

We know Maria took seven hours, but we absolutely have no clue about Maria's average speed. On the other hand, Sarah average speed was 50 mph, which is derived from 1/3 x 60 mph + 2/3 x 45 mph = 50 mph. Yet, we still do not know how many hours Sarah was driving at 50 mph. So we have two missing values here: Maria's average speed and Sarah's driving hours. Either one would be good to answer the question, since they were driving the same distance.

(1) is insufficient because it gives us nothing about Maria's average speed or Sarah's driving hours.

(2) Okay, so we have two scenarios: Maria's speed is 10 mph faster than Sarah's or Maria's speed is 10 mph slower than Sarah's.

In the first scenario, assuming that Maria's speed is 60 mph (50 mph + 10 mph), we arrive at the total distance of 60 mph x 7 hours = 420 miles covered by Maria. Because they drove the same distance, it implies that the total distance they covered would be 840 miles.

In the second scenario, Maria's speed was 40 mph (50 mph - 10 mph). Therefore, the total distance covered by Maria was 40 mph x 7 hours = 280 miles. The total distance they covered would be 560 miles.

Therefore, the statement (2) is insufficient.

(3) However, combining both statements, we now know that Sarah took less time than Maria (Sarah is faster than Maria), thus Maria is slower than Sarah by 10 mph, which takes us to the second scenario of 40 mph (Maria's speed). As a result, the total distance they covered would be 560 miles.

The answer is C.

Thank you!