2 cars are 120 miles apart.If both cars go at a constant

Question

2 cars are 120 miles apart.If both cars go at a constant speed with one of them going at 30/mph and the other 40/mph - how far apart will the 2 cars be in exactly 1 hour before they meet?

a. 35
b. 40
c. 70
d. 85
e. 90

MA · Answer

do we need to calculate? because these cars go 70 miles/hour.

Antmavel · Answer

c.70

first, both cars will meet :
40x + 30x = 120 ; x = 12/7h 

means that 1h before they meet both cars would have driven 12/7-7/7 = 5/7h

for 40mp/h car -> 40*5/7 = 200/7
for 30mp/h car -> 30*5/7 = 150/7

they will drive for 50 miles but the difference is 120 so there is still 70 miles to cover

however, if you ignore the fact that there are 120 miles apart, you can find 70 considering that both cars begins at the same location, how far both cars will be from each other after 1h ? 30+40 = 70. I really assume it is a lucky number and that's pure coincidence. I can't see any other reason. I doubt this problem would be given on Gmat, or at least the lucky number would'nt be the real OA, they would have given 20 mph and 80mph driving 2hrs for exemple...they don't want you pick the easiest stupid number (1h and 30+40) an answer correctly to a more complex problem

Rupstar · Answer

Does anyone know if the cars are travelling in opposite directions or in the same direction...because that should change the answer

Rupstar · Answer

Two choices...
since this question doesnt clearly state whether they are heading in opposite directions towards each other or away from each other or in the same direction, its difficult to decide.
Since it isnt stated that they are going in opposite directions, and that is usually rare/less common in the speed problems
we have ption 1 in which they head towards each other...as Antmavel chose...this is usually what you see alot of on the 
GMAT speed/distance/time problems.
Using the same process as Antmavel i too got 70 but now considering that NOTHING IS SAID about direction
the first inclination is that they are 120 miles apart heading in the same direction.

According to that hypothesis;
in an hour one moves 40 miles and the other 30, initial distance gets dropped to 110 miles, so every hour on the hour one car closes the gap by 10 miles.
From the meeting point the distance between them an hour before would be 10 miles (by the same logic)
since this is not a choice, they probably are going towards each other, either the author of the quesiton missed something or the question is badly phrased

HongHu · Answer

Good thinking. And there's the chance that they never meet if they both go the other direction. Although this means the question is not well defined, if you met a question like this in the test, you would have to work in the range that is given, in other words since 10 and infinite are not included in the choices you pick the only possible correct answer 70.

MA · Answer

i agree with you. definitely a GMAT DS thinking.

ywilfred · Answer

let n be the time taken for both cars to meet.

Then 40n + 30n = 120 
n = 12/7

Since we want the distance 1 hr before they meet, the cars must have travelled for 5/7 hour

For the car travelling at 40km/h - would have covered 28 4/7 km
For the car travelling at 30km/h - would have covered 21 3/7 km
In total they cover 50km

So they are now 120-50 = 70km apart.

MA · Answer

I am withdrawing my previous statement because the question mentioned "  MEET  ". if these cars are meeting after 1 hour they must be travelling towards each other because their speeds do not allow them to travel in the same direction.

2 cars are 120 miles apart.If both cars go at a constant

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