If a car traveled from Townsend to Smallville at an average

Lets distance be x miles between 2 cities (lets say T and S).
From T to S speed = 40 mph so time taken = x/40 hrs
From S to T spees = 60 mph (50% less time) so time taken = x/60 hrs

Total time taken = x/40 + x/60 = x/24 hrs
Total distance travelled = 2x miles

So avg speed = 2x/(x/24) = 48 mph

Instead of x you can solve this by taking 40 miles as distance.

So statement 1 is sufficient.

hi,

let say distance between T and S be X miles
time take to cover from T-S=X/40

statement 1==>time for T-S=1.5(time from S-T)
THEREFORE==>X/40=1.5(T)
THEREFORE ==>T=X/60

Average speed =total dist/total time

==>total dist=X+X=2X
AVG SPEED=2X/(X/40+X/60)=48
HENCE SUFFICIENT.

HOPE IT HELPS

Small correction: the average speed would be 48 mph, not 50.

If a car travelled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend along the same route later that evening, what was the average speed for the entire trip?

Distance/Time = average speed

D/T = 40

(1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend.

We're looking for the total time here. In other words, we want to know the total distance/total time (the distance to and from and the speed to and from) We know that the distance is the same for both trips so that can be represented as 2d. Because we don't know the distance, to find time we will have to get distance/speed = time.

Total distance = 2d
Total time = time from T to S = time from S to T. Time = distance/speed. We know that the speed from T to S was 50% more than from S to T which means that the speed from S to T was 50% greater (i.e. 40 + 40*.5 = 60MPH)

Total Distance/Total Time = total average
2d/([d/40] + [d/60]) = total average
2d/([3d/120 + [2d/120]) = total average
2d/(5d/120) = total average
2d * 120/5d
240d/5d
d=48

If we plug 48 into d/t = 40 then we can get a value for t.
SUFFICIENT

(2) The route between Townsend and Smallville is 165 miles long.
We know that the distance is 165 which means that the round trip is 330 miles. The problem is, we are looking for average speed and we have no idea what speed was done on the return trip.
INSUFFICIENT

(B)

VeritasPrepKarishma

If a car traveled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend later that evening, what was the average speed for the entire trip?

(1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend.
(2) The distance from Townsend to Smallville is 165 miles.

How can the answer be A folks?



mam
in this you said Ratio of time in the two cases
T to S: S to T= 3:2 how mam? can u explain in bit detail plz?

The trip from T to S took 50% longer. So if trip from S to T took 2 hrs, the trip from T to S took 50% more that is 50% of 2 hrs more i.e. 1 hour extra. So it took 2+1 hours i.e. 3 hrs. This gives a ratio of 3:2. Time taken from T to S : Time taken from S to T. The actual time taken could be anything. 6 hrs and 4 hrs or 9 hrs and 6 hrs etc.

Posted from my mobile device

Even I used to be confused with this concept but a through reading of speed time concept from magoosh helped me clear my basic flaws in understanding.

Coming to the question:
Speed distance has just one killer concept
s=d/t

Which means s is inversely proportional to time.
now it is given t1=1.5t2
therefore s1 which is inversely proportional will be 2/3s2
s1=40 hence s2=60

Apply the average speed formula 2d/(d/40+d/60)
take d common and cancel it .

Voila! you got the answer

Please give a kudos if you liked my answer.

my 2 cents:

We are told that a car traveled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend the same evening. Right away, we know the distance to Townsend and back are equal. Thus, let distance = 2d.

(1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend.

average speed = total distance / total time

average speed = 2d / (d/40 + d/60)

We are able to solve for distance. D = 48. Statement 1 is sufficient.

(2) The distance from Townsend to Smallville is 165 miles. We are not able to determine the speed of the car returning from Smallville. Insufficient.

Answer is A.

What is the return trip in this? Smallville to Townsend? Or the other way around?

Posted from my mobile device

My problem with this question is that we Assume that the car returns along the same route, while nowhere in the question is any detail about the route from S---to----T mentioned. If iam correct, we can never assume anything when it comes to DS questions. For this reason i had E as answer

In the question below, it is clearly mentioned in one of the statement that the there and back route is the same(along the same route). so here if we use the same logic as the question above i.e making assumption, the answer would be wrong.

https://gmatclub.com/forum/brian-takes- ... 88967.html

Can anyone please shed some light on my confusion about this question.

Thanks in advance!

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