kevincan wrote:

A train always travels at one of two speeds: 160 km/hr in rural areas and 40 km/hr in urban areas. Was its average speed from A to B greater than 100 km/hr?

(1) More than 2/3 of the distance from A to B is through rural areas.

(2) The distance from A to B is more than 1000 km.

Kevin Armstrong

Manhattan Review

Let's do it step-by-step.

What is average speed? It is the total distance travelled divided by the total time. If we imagine that a car traveled half the distance with the speed 50 mph, and the other half with the speed 100 mph, how to get the average speed?

Let's put 40 miles as the total distance. Hence, 20 miles is 1/2 of it.

The first half was covered in 0.4 of an hour (i.e. in 24 min.) The second one - 0.2 of an hour (12 min.). Therefore, the total time equals 0.6 of an hour, and the total distance is 40 miles.

As a result, the average speed is 40 miles/0.6 of an hour, the average speed is about 66.6(6) mph.

Now let's look at the problem. If we know that more than 2/3 of the distance is made with the speed 160, let's just put some numbers.

Distance = 300. 200 with 160mph, 100 - 40 mph. The average speed is MORE than 80 mph (it would be 80 if EXACTLY 2/3 of the route is covered with superspeed

) We don't know, how much is the exact number. It can be greater then 100, if, for example, the train travel 295 "rural" miles and 5 urban (average speed equals 155 mph). 295 out of 300 miles is still "more than 2/3 of the distance".

As a result, A is useless. IF exactly 2/3 of the distance mean more than 100 mph, anyway, then we would use it. However, it does not.

Finally, B is useless, since the average speed is not bound to the total distance directly, but through the time spent.

My answer is E.

Please, fell free to correct any of my grammar mistakes. I am Russian, and for the moment I am fiercely trying to remember anything about English and its grammar.