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

Stmtn 1 -
if total is assumed as 1 , we can find the average speed .
Comes to 80 miles/hr.

Stmtn2 - redundant information . need to know the break up of time or distance.

A

Ans is A.

Logic of the question suggests that we need only know what fraction of the entire trip was rural vs not, in order to find the actual time.

1st premise provides us exactly this information.

2nd premise is a dud.

By the way, this is a great candidate for time saving by avoiding unnecessary math. If you can visualize this problem, you need not write any math down to solve it -- give yourself more time for the other calc intensive problems down the road.

Another GMAC favorite in this genre is "did the train ever exceed speed X during such and such trip?". Well, maybe for a split second the train gassed it up and went super duper fast, while noone was looking... the answer to this question is usually E, because you usually cannot know if there was a split second surge in speed while the rest of the trip was normal.

from basics, what i know is that in order to find the average speed we need to find the distance and time only.
we do not have the time it took the train to travel with different rates of speed so. we can find the time using both of the statements.
i think it is C. speed is >40 mp/hour
will post the explanation if it is the correct answer.

kevin doesnt post simple questions?!

Ans. is E

From stat 1 we can get the min speed av but setting the distance to 2/3 when the train travels at 160 Km/h.

this gives us an av. speed of 80 Km/h; indeed av speed = distance/time.
= d / [(2d/3x160) + (d/3x40)]

Max speed is when the train travels all the time in rural area => speed = 160.

Thus stat. 1 is not sufficient

Stat. is not sufficient as well.

Somebody is too confident here

distance = time x speed (dont forget that)

so av. speed = total distance / total time (what I have calculated)

however 160 x (2/3) doesn't mean anything since it's speed x distance ...

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.

[quote="kevincan"]Perhaps the nicest way is to see what the average speed would be if fraction f of the trip were through rural areas.[/quote]


ooops! sorry guys ... My brain short circuited!

get clear E for this question,

Average speed= total distance/ total time=D/T
D=dr+du
T=total time=time in rural area+time in urban area
T=dr/40+du/160

A=D/(dr/40+du/160)

A=D*160*40/ (dr*40+du*160)=D*160*40/(dr+4*du)*40

thus

A=D*160/(dr+4*du)

(1) INSUFF

(2/3)D<dr, then (1/3)D>du, for convenience lets assume dr=(2/3)D and du=(1/3)D

A=D*160/((2/3)D+(1/3)*4*D)
A=160/(2/3+4*1/3) --------------------> whatever the total distance is THIS will be the equation for average speed

160/(2/3+4*1/3) =~27, to cancel previous assumption, lets calculate
160/(0,70+0,3*4)=~84

thus Average speed>27------------> average speed could be more than 100, could be less.

(2) INSUFF

obviously insuff

both) INSUFF

A=160/(2/3+4*1/3) --------------------> whatever the total distance is THIS will be the equation for average speed, thus yeilds the same result as A

calculations is a must for tough DS...