If a car traveled from Townsend to Smallville at an average

Question

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?

KarishmaB · Accepted Answer

A couple of basics: 1. Average Speed = Total Distance/ Total Time 2. Average Speed = Weighted Average of different speeds where 'time taken' is the weight 3. If equal distances (say d) are traveled at different speeds, a and b, average speed = 2d/ = 2ab/(a+b) In this case, average speed is independent of 'd', the distance. 4. If speeds a and b are maintained for equal time intervals, say t, average speed = (at+bt)/2t = (a+b)/2 In this case, average speed is independent of 't', the time interval. Given: Car travels equal distances. Speed in first case is 40 mph. We need the speed in the second case to get the average speed (given by 2*40*b/(40+b)) (1) Ratio of time in the two cases T to S: S to T= 3:2 Then ratio of speed in the two cases = 2:3 We know the speed from T to S = 40 Then speed from S to T must be 60 Since we have the value of b (= 60) i.e. the speed while coming back, we can easily find the average speed.. Sufficient. (2) As we discussed, distance traveled doesn't affect average speed in this case. Not sufficient Answer (A) TSD Basics are discussed here: https://youtu.be/7ASEIvxYPCM

Bunuel · Answer

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?

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

Time from T to S 3/2 of that from S to T, thus
Speed from T to S 2/3 of that from S to T. Thus speed from S to T = 60 mph.

Now,  (average \ speed)=\frac{(total \ distance)}{(total \ time)}=\frac{2d}{\frac{d}{40}+\frac{d}{60}} , where d is the distance between S and T --> d reduces --> we can get the average time. Sufficient.

(2) The route between Townsend and Smallville is 165 miles long. We know nothing about the speed from S to T. Not sufficient.

Answer: A.

Hope it's clear.

SwapnilRanadive · Answer

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.

blueseas · Answer

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

Bunuel · Answer

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

WholeLottaLove · Answer

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/(  +  ) = total average
2d/( ) = 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)

VICKY69 · Answer

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?

KarishmaB · Answer

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.

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Posted from my mobile device

AmritaSarkar89 · Answer

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.

manishtank1988 · Answer

my 2 cents:

Basshead · Answer

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.

BodhiChatterjee · Answer

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

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GinoRako · Answer

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!

riri3026 · Answer

KarishmaB

The reason that the second statement is NF, is cause there is no distance in the formula. But I wanted to get some assurance about the fact that -Avg Speed = Total Distance/ Total Time is also not sufficient to solve this particular question as no time has been given in St II.

KarishmaB · Answer

Yes, that is correct. If we have the time taken to cover the second leg of the journey (along with the distance) then we would have been able to find the average speed. 
The point is that the ratio of time taken on each leg is enough to give us the total average speed. We don't need the distance travelled because we know that it is equal on both the legs of the journey.

Rebaz · Answer

Bunuel   KarishmaB

We always get told that we cannot make assumption on DS. For this reason i chose E as answer.

But to my surprise, you guys assume that the Car drove back along the same path. How is that even possible?

Nowhere in the statements is information given about the route the car took on it's return?

Can you elaborate on that?

Thanks in advance!

KarishmaB · Answer

The intent of the author was clearly to say that both legs of the journey are the same distance (else it becomes just too simple) but I agree - in actual GMAT questions it would be mentioned that they travelled along the same route. That is why if you notice Bunuel has re-written the question himself:

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?

ektalakra · Answer

the question mentions that avg speed for 1st trip is 40 mph. normally we take constant speed while doing calculations . there are times when avg speed is not same as const speed. in exam how do i know that the avg speed given is to be considered as the const speed and go ahead with the calculations

Bunuel · Answer

When the question says "the car travelled at an average speed of 40 mph," that is all you need. It means the entire leg of the trip can be treated as if the car moved at 40 mph constantly. So yes, you can safely use t = d/40.

If a car traveled from Townsend to Smallville at an average

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If a car traveled from Townsend to Smallville at an average

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