Maria left home 1/4 hour after her husband and drove over the same rou

This is a very good question based on relative speed.

(1) Maria drove 60 miles before overtaking her husband.
No info about the speeds. NOT SUFFICIENT.


(2) While overtaking her husband, Maria drove at an average rate of 60 miles per hour, which was 12 miles per hour faster than her husband's average rate.
As we know both speeds, we can find the distance travelled by husband at the moment Maria started.
hence relative distance is known, also relative speed.
SUFFICIENT.

Answer B

(complete solution NOT required for Data Sufficiency:
Maria speed = 60miles per hour, Husband speed = 60-12= 48 miles per hour
Relative distance = distance covered by husband when Maria started = 48*1/4 = 12miles
relative speed = 60-48=12miles per hour
Time = 12/12 = 1 Hour
But No need to solve )



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Solution

Step 1: Analyse Question Stem

• Let us assume that Maria took t hours to overtake her husband.

o Total time for which her husband drove, before she could take over him \(= (t+\frac{1}{4})\) hours.

We need to find the value of t.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: Maria drove 60 miles before overtaking her husband.

• According to this statement: total distance travelled by Maria to overtake her husband = 60 miles
• Maria’s speed (in miles per hour) \(* t = 60\)
• However, we don’t know her speed.

Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.
Statement 2: While overtaking her husband, Maria drove at an average rate of 60 miles per hour, which was 12 miles per hour faster than her husband's average rate.

• According to this statement: Maria’s speed = 60 miles per hour

o Her husband’s speed \(= (60 -12) = 48\) miles per hour.
• At the time she overtook him, both have travelled same distance.

o So, \(60*t = 48*(t+\frac{1}{4})\)
o Thus, we have one equation and one variable, we can easily solve to get the t.

Hence, statement 2 is sufficient.
Thus, the correct answer is Option B.
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Target question: From the time she left, how many hours did it take Maria to overtake her husband?

Statement 1: Maria drove 60 miles before overtaking her husband.
Lots of necessary information is missing here. Consider these two possible scenarios
Case a: The husband's speed is 48 mph. which means he has a 12-mile lead when Maria starts driving. If Maria's speed is 60 mph, she will overtake her husband in 1 hour (and she will have driven 60 miles in the process). In this case, the answer to the target question is it takes 1 hour for Maria to overtake her husband
Case b: The husband's speed is 60 mph. which means he has a 15-mile lead when Maria starts driving. If Maria's speed is 80 mph, she will overtake her husband in 0.75 hours (and she will have driven 60 miles in the process). In this case, the answer to the target question is it takes 0.75 hours for Maria to overtake her husband
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: While overtaking her husband, Maria drove at an average rate of 60 miles per hour, which was 12 miles per hour faster than her husband's average rate.
So, Maria's speed = 60 mph
And her husband's speed = 48 mph.
IMPORTANT: At this point we need not perform any lengthy calculations. We need only recognize that we COULD conduct an experiment with all of the given information, and that such an experiment would tell us exactly how many hours it took Maria to overtake her husband, which means we COULD answer the target question with certainty. So, statement 2 is SUFFICIENT.

Here's what I mean:
We all head over to Maria's house. First, we tell Maria's husband to start driving on some route at a speed of 48 mph. 15 minutes (aka 1/4 hours) later, we start a stopwatch and tell Maria to start driving on the same route at a speed of 60 mph. Once Maria overtakes her husband, we stop the stopwatch, and we now know exactly how long it took Maria to overtake her husband.

Answer: B

Cheers,
Brent

I have problem with the word ''while", which in my opinion means the moment Maria overtake her husband. This is in my opinion totally different from her speed before overtaking her husband and her husband's speed before been overtaken by Maria. This is why i have hard time slecting answer choise B.

Can someone please shed more light on my confusion with regard to statement 2 and the word ''While" in this contex?

Thanks in advance!

you are right.
'while" means the moment Maria overtakes her husband. but since average speed is given , it doesn't matter whether her speed is lower or higher.
Average speed takes care of the earlier changes.

we need the total time taken by her the travel the relative distance.

Average Speed = Total Distance /Total time
( ups and down in speed doesn't matter)


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Maria left home 1/4 hour after her husband and drove over the same route as he had in order to overtake him. From the time she left, how many hours did it take Maria to overtake her husband?

(1) Maria drove 60 miles before overtaking her husband.
(2) While overtaking her husband, Maria drove at an average rate of 60 miles per hour, which was 12 miles per hour faster than her husband's average rate.

Nice C trap!

(1) Insufficient, we don't know the rate of Maria's husband.
(2) Sufficient, Since we know the rate of Maria and her husband we are able to find in how many hours she overtakes her husband.

Answer B

Posted from my mobile device

Since, Maria overtook her husband it means they both covered same distance.We need to find the time they took to meet.
Speed(M).Time(M) = Speed(H).Time(H)
Here M stands for Maria and H for husband.
(1) Maria drove 60 miles before overtaking her husband.- Not sufficient/Not needed.
(2) While overtaking her husband, Maria drove at an average rate of 60 miles per hour, which was 12 miles per hour faster than her husband's average rate.-
Speed(M).Time(M) = Speed(H).Time(H)
60(T) = 48(T+1/4)
This equation gives us time, which is asked in the question.Hence, B is sufficient.
Hope it helps.

EEEEEEEEEEEEEEahaaaaaaaaaa: Making it simple
Given data: M left after 15 mins of H.
----> she has to cover 15 mins of husband distance+some distance her husband covered meanwhile
TIME to overtake=x=?

1) Distance=60 miles--> clearly insufficeint

2)Ms=60mph; Hs=48mph; say x be the time when they meet
---> H distance= 48*(1/4+x)
---->M distance=60*x
They will meet when both distances are equall --> Hd=Md--> 48*(x+1/4)=60*x
We can find x from above equation.

Therefore B is the answer

HOPE THIS HELPS

THANKS

time = distance / speed

(1) Maria drove 60 miles before overtaking her husband

time = 60 / speed

We don't know the speed Maria drove. Thus, this statement is insufficient.

(2) While overtaking her husband, Maria drove at an average rate of 60 miles per hour, which was 12 miles per hour faster than her husband's average rate.

t = d / 60

We known that the husband started 1/4th an hour earlier and his speed is 12 miles slower than Maria's speed. Therefore:

t - 0.25 = d / 48

We are able to solve for t, which is 1.
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Trying to solve it through my understanding of relative speed.
NOTE: 2 objects moving in the same direction reduce the distance b/w them at the following rate: SPEED of a-SPEED of b

Statement 1: NS
Statement 2: Maria's Husbands speed: 48 & Maria's Speed:60

Time = D/relative speed.
NOTE: here D =12 (as per the question and the information is given in statement 2 this is what Maria's husband would have covered in 15 minutes)

time to overtake= 12 miles/ 12 miles /hr =1 hr
Hence, statement 2 is sufficient

you are right.
'while" means the moment Maria overtakes her husband. but since average speed is given , it doesn't matter whether her speed is lower or higher.
Average speed takes care of the earlier changes.

GMATBusters

CAN YOU ALSO EXPLAIN REASONING MENTIONED FOR BELOW QS?

https://gmatclub.com/forum/stations-x-a ... 77177.html

Here, the avg speed at the time of passing is different from avg speed during the whole trip.

Avg Speed = total distance travelled / total time taken.

the time at which Avg speed is calculated, consider the travel before that only, unless specified explicitly.

Hence, the avg speed at the time of passing might be different from avg speed during the whole trip.

if you have any doubt, let me know.


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It boggles my mind that we think B is the answer. As written, we have absolutely no information about the husband's speed before Maria leaves. At no point are we told that the husband's speed is constant. There is no justification for assuming that the husband's speed was, on average, 48 mph during the 1/4 hour before Maria left.

Maria's husband could have traveled at light speed for some number of seconds, then sat there and waited the necessary amount of time so that his average speed became 48 mph by the time Maria caught up.

Is this missing some part of the OG phrasing? Because B is definitely NOT the answer here.