If a car traveled from Townsend to Smallville ...

[gettoalok]

Following is a DS question in the free MGMAT CAT test :
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.

I'm not able to understand the explanation given :
(1) SUFFICIENT: This allows us to figure out the average speed for the return trip. If the return time was 3/2 the outgoing time, the return speed must have been 2/3 that of the outgoing. Whenever the distance is fixed, the ratio of the times will be the inverse of the ratio of the speeds.

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Shouldn't the return time be less than the outgoing time? In statement "1", its given that trip from Townsend to Smallville(outgoing) took 50% longer than the trip from Smallville to Townsend(return).

Hence return time should be t and outgoing time should be 3t/2 ?
Please correct me if I'm wrong.

Also, I don't understand the concept "Whenever the distance is fixed, the ratio of the times will be the inverse of the ratio of the speeds."

[lynncf]

1) states that from town T to S took 50% longer (in terms of time), thus the rate must be slower.

the inverse relationship between rate and time is defined as, for example, if the time is 2 hours, the rate must be 1/2.

[jerly_vivek]

for easy calculation lets say the distance b/w T and S is 40 miles.
So for T->S took 1 hr. That means from S->T took 40 minutes. Now we can caluclate average return speed. So if we have both forward (x) and backward(y) speed, we can easily calcualte avg. speed.(2xy/(x+y))

[esledge]

Also, I don't understand the concept "Whenever the distance is fixed, the ratio of the times will be the inverse of the ratio of the speeds."

General relationship: R*T = D

If R increases by a factor of 3 (i.e. times 3), T would have to decrease by a factor of 3 (i.e. times 1/3) in order to keep D constant.