Maria drove a distance without stopping such that she covered first

Question

Maria drove a distance without stopping such that she covered first 1/3 of distance in 3 hours and remaining distance in 4 hours. Sarah drove the same distance without stopping such that she drove for first 1/3 of total time at a speed of 60 mph and for remaining time at a speed of 45 mph. What is the total distance that each of them has covered?

(1) Sarah covered the distance in lesser time than Maria.

(2) Difference between the average speeds of Maria and Sarah is 10 mph.

(1) Sarah covered the distance in lesser time than Maria.

(2) Difference between the average speeds of Maria and Sarah is 10 mph.

sahuiitd · Accepted Answer

Let the Total distance Travel by both of them is D miles.

For Maria: (D/3)=S * 3 & (2D/3)=S' * 4
For Sarah: D'=(T/3) * 60 & D"=(2T/3) * 45..... We get D'+D"=D=50T

Statement 1: Time by Sarah < Time by Maria
 (D/50) < 7
 D < 350 Miles Not Sufficient
Statement 2: Here there are 2 cases:
 Case 1: M=S+10
 (D/7)=(D/T)+10
 (D/7)= 50+10........D=420 Miles
 Case 2: M=S-10
 (D/7)=(D/T)-10
 (D/7)= 50-10........D=280 Miles
 Not sufficient.
Both Statement 1 & 2

We get D=280 Miles.

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Princ · Answer

amanvermagmat

I have doubt about the statement 2.

Let  Av_{Maria}  be the Average speed of Maria and  Av_{Sarah}  be the average speed of Sarah

Does Statement 2 means 
 |Av_{Maria}- Av_{Sarah}| = 10  or  Av_{Maria}- Av_{Sarah} = 10

Source: GMAT Club Math Book, Page: 34

According to GC Math Book,Statement 2 means  Av_{Maria}- Av_{Sarah} = 10

sunilnitw08 · Answer

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

amanvermagmat · Answer

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.

amlan2018 · Answer

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

arj93pop · Answer

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

LeonidK · Answer

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

amlan2018 · Answer

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.

deddex · Answer

Bunuel   gmatbusters   VeritasKarishma  please can you help in this?

GMATBusters · Answer

deddex , 
Solution is as per sketch:

GMATBusters · Answer

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

Quynhsatoh · Answer

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

bobsibusaa · Answer

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!

bumpbot · Answer

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Maria drove a distance without stopping such that she covered first

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