IQ test question

[Everest]

I got 24 miles.

They were driving along the coast. One driver turned left and just as she was about to reach the 8 mile point, went over a cliff and sank in the sea.

*It was a woman using her satnav*

 

[Lord Bracknell]

Bit bored this morning so took an online IQ test, this was one of the questions, can somebody tell me what is the answer and why. cheers chaps.



Two cars start off at the same point on a straight highway facing opposite directions. Each car drives for 6 miles, takes a left turn, and drives for 8 miles. How far apart are the two cars?

2 miles

11 miles

14 miles

20 miles

26 miles

There's always the option of asking the question "when?".

If the two cars start at the same point, they are no distance apart when they start. Why has everyone assumed that the question refers to the finish of the driving?

 

[Sajerz]

I scored 126

 

[Barrow Boy]

Well, according to:

http://bellsouthpwp.net/a/g/agent459/iqresult.pdf

To solve this problem, you may want to get a piece of scratch paper. Draw a
point on your paper that indicates the starting location of both cars. From here,
draw a line that is 6 units long in opposite directions from the starting point
(you decide what a unit is; if you used ? inch as your unit, the distance that on
car goes would be 1 ? inches). The line you end up with should be 12 units long
and straight. For the purposes of this example, let's say that line runs East-
West. From there, each car turns left and drives 8 miles (units). In this case,
one of the cars would have driven due north and the other would have driven
due south. Your illustration should look kind of like a "Z". Now you know the
location of each car.
To find out how far apart they are, use the Pythagorean Theorem, which says
that the square of the longest side (hypotenuse) of a right triangle is equal to
the sum of the squares of the other two sides. In this case, the distance
between the two points is the hypotenuse of a right triangle. The distance the
cars drove away from each other in the East-West direction was 12 miles, so
one side of the right triangle is 12 units long. The distance the cars drove away
from each other in the North-South direction was 16 miles, so the other side of
the right triangle is 16 units long. Plugging these values into the Pythagorean
Theorem, you should get:
12^2 + 16^2 = SQRT c
144 + 256 = SQRT c
400 = SQRT c
20 = c
The cars are 20 miles apart

Why did you do an IQ test?

I cheated and did it using a ruler (half inch to 1 mile) if you measure the distance between the two final positions of the cars (as the crow flies) it's 10 inches therefore 20 miles.

Blimey, talk about making hard work, and I thought Pythagoras was a town in Lesbos !

 

[Tricky Dicky]

There's always the option of asking the question "when?".

If the two cars start at the same point, they are no distance apart when they start. Why has everyone assumed that the question refers to the finish of the driving?

Also, it didn't state that they both drove forward. One could have gone in reverse

 

[Trufflehound]

Blimey, talk about making hard work, and I thought Pythagoras was a town in Lesbos !

You're confusing it with Pie Fag 'n' Rosé - the discerning lesbian's top night out.

 

[Fungus]

Also, it didn't state that they both drove forward. One could have gone in reverse

If you "turn left" after 6 miles in reverse, you'd then be going in the opposite direction to the other car. So, the answer is 16 miles. They should've put that on the list.

Of course, they could *both* go in reverse. But they might hit each other.

 

[Tricky Dicky]

If you "turn left" after 6 miles in reverse, you'd then be going in the opposite direction to the other car. So, the answer is 16 miles. They should've put that on the list.

Of course, they could *both* go in reverse. But they might hit each other.

If they started from the same point, what's going on there - was one on top of the other, or is it some kind of Quantum Mechanics particle state ?? We need to know these things.

 

[NMH]

I think all of you are overlooking an important factor inherent in this calculation.

Pythagoras was working on a flat plane, and the theorem that he discovered, where the square on the hypotenuse is equal to the sum of the squares on the other two sides, works on paper.

However..... the IQ test here, has placed two cars on a highway, presumably on a planet somewhere. Planets normally being spherical, the actual distance between the cars would be less than the distance that Pythagoras' theorem calculates on a flat plane. To know the correct answer, we would have to know the geology of the area these cars travelled over.

Any questions?

 

[Tricky Dicky]

I think all of you are overlooking an important factor inherent in this calculation.

Pythagoras was working on a flat plane, and the theorem that he discovered, where the square on the hypotenuse is equal to the sum of the squares on the other two sides, works on paper.

However..... the IQ test here, has placed two cars on a highway, presumably on a planet somewhere. Planets normally being spherical, the actual distance between the cars would be less than the distance that Pythagoras' theorem calculates on a flat plane. To know the correct answer, we would have to know the geology of the area these cars travelled over.

Any questions?

Yes, if one of them enters a worm-hole (assuming it survives the singularity) - can he arrive before the other one leaves ?

 

[Fungus]

Any questions?

Would it be greener if they shared one car?

 

[maffew]

I think all of you are overlooking an important factor inherent in this calculation.

Pythagoras was working on a flat plane, and the theorem that he discovered, where the square on the hypotenuse is equal to the sum of the squares on the other two sides, works on paper.

However..... the IQ test here, has placed two cars on a highway, presumably on a planet somewhere. Planets normally being spherical, the actual distance between the cars would be less than the distance that Pythagoras' theorem calculates on a flat plane. To know the correct answer, we would have to know the geology of the area these cars travelled over.

Any questions?

hmmm

good point.

Ok this gonna take a bit more working out. I think we'll have to assume that the curve is equal on both sides and no hills involved or it'll get silly

The problem is we need to know what direction they are travelling in and where they are starting from. Cos to work out the above we need to know the diameter of the earth which is different on the equator than it is pole to pole

So lets say they are starting on the equator from the same starting point, ones driving straight east, ones driving straight west. The terrain is the same. They are both going forward. The diameter of the earth is 12,756.32 km at this point

the rest is the same as before

 

[NMH]

hmmm

good point.

Ok this gonna take a bit more working out. I think we'll have to assume that the curve is equal on both sides and no hills involved or it'll get silly

The problem is we need to know what direction they are travelling in and where they are starting from. Cos to work out the above we need to know the diameter of the earth which is different on the equator than it is pole to pole

So lets say they are starting on the equator from the same starting point, ones driving straight east, ones driving straight west. The terrain is the same. They are both going forward. The diameter of the earth is 12,756.32 km at this point

the rest is the same as before

Calculating the distance between the cars can be done by taking the radii from the earth's centre to both cars on the surface, then draw a straight line between them and calculate the length of that line.
Off you go.

 

[NMH]

Would it be greener if they shared one car?

They should make these iq tests greener, good point

 

[Nibble]

Would it be greener if they shared one car?

Impractical if they are going in differant directions.

 

[Yoda]

Why all the long winded way?

All I did was how far apart they were after the first part. Then added half the distance from the second as if they had started in the same place.

(6*2)+8=20.

 

[Djmiles]

Why all the long winded way?

All I did was how far apart they were after the first part. Then added half the distance from the second as if they had started in the same place.

(6*2)+8=20.

Already been explained

 

[lost in london]

How do we know that the 8 miles they drove after turning left was in a straight line? Chances are they turned onto a country lane or maybe an A road, which in all probability had some bends in it.

 

[maffew]

Why all the long winded way?

All I did was how far apart they were after the first part. Then added half the distance from the second as if they had started in the same place.

(6*2)+8=20.

NO WAY!!!

 

[maffew]

Calculating the distance between the cars can be done by taking the radii from the earth's centre to both cars on the surface, then draw a straight line between them and calculate the length of that line.
Off you go.

OK, think this is the real answer

Answer should be slightly less than 20, all units the same. Assuming the Earth is spherical it's this
2*(12756.32/2)*Sin(((20*1.609344)/(12756.32*pi)*360)/2)

=19.9999918 km

but cos the diameter is smaller North to South it's a bit less but i can't do that