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
Do you know the answer? I've been working on it since forever! If you do know the answer, can you share? And please include a rough explanation. Not a long one. Many thanks.
2007-10-27 09:27:45 · 11 answers · asked by XbabynovaX 5 in Science & Mathematics ➔ Mathematics
20 miles: draw it out on a sheet of paper in centimetres and it is easy.
2007-10-27 09:40:18 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Oh all right, I'll explain Sahsjing's correct answer of 20 miles. Imagine that the highway has farm plots 6 miles long (along the highway) and 8 miles wide (perpedicular to the highway). The two cars start at the intersection of 4 such 6x8 farm plots, so that by the time they both drive 6 miles on the highway and each make a LEFT turn and go 8 miles away from the highway, they are now at diagonally opposite corners of a set of four 6x8 farm plots. In other words, they're 12 miles apart in one direction, 16 miles apart in another. Using the pythagorean theorem you can compute the diagonal distance between the two as follows:
20 miles = â(12² + 16²)
I believe the source of your confusion is that you have to realize that both cars, in both making a LEFT turn, go in OPPOSITE directions from the main highway.
2007-10-27 16:36:50 · answer #2 · answered by Scythian1950 7 · 1⤊ 0⤋
Use Pythagoras. Each car will be sqrt(6^2 + 8^2) = 10 miles from the starting point, so the cars are 20 miles apart.
2007-10-27 16:33:27 · answer #3 · answered by Helen B 5 · 0⤊ 0⤋
20 miles.
The cars can basically be seen as being separated by the hypotenuse of a right triangle, where one leg is comprised of the distance they drove before taking the left turns (a total of 12 miles) and the other is comprised of the distance they drove after the turns (a total of 16 miles).
To get the answer, now, you can either apply the pythagorean formula and get c^2 = a^2 + b^2 = 12^2 + 16^2 = 400; c = â400 = 20, or you can just recognize that this right triangle is simply four times a 3-4-5 triangle and just take 4*5=20.
2007-10-27 16:33:16 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Let's look at it step by step ...
When the head in opposite directions for 6 miles each they're 12 miles apart when they turn. Let's say this is on the x axis.
When they both turn left they once again are heading in opposite directions this time for 16 miles on the y axis.
(The one that was heading east now heads north, while the one that was heading west now heads south)
So to fine the distance apart they are its ...
c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400
c = 400^(1/2) (aka Square Root of 400 )
c = 20
2007-10-27 16:38:25 · answer #5 · answered by b_plenge 6 · 0⤊ 0⤋
20 miles
Each car is sqrt(6^2+8^2) = 10 miles from starting point, so they are 20 miles apart.
2007-10-27 16:31:41 · answer #6 · answered by ironduke8159 7 · 0⤊ 0⤋
20 miles directly.
Due to the fact both cars took a left turn and drove 8 miles, they form a right angled triangle and you have to find the hypothenese.
sqrt(8^2+6^2)= 10.
10*2=20 miles apart.
2007-10-27 16:40:41 · answer #7 · answered by Phantom 2 · 0⤊ 0⤋
20 miles
2007-10-27 18:17:12 · answer #8 · answered by LULU 2 · 0⤊ 0⤋
20 miles
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Ideas: Use 6-8-10 Pythagorean triple, and double the 10.
2007-10-27 16:30:22 · answer #9 · answered by sahsjing 7 · 0⤊ 0⤋
boy is there some smart people in here i got lost after 12 +16 miles
2007-10-27 16:40:18 · answer #10 · answered by Anonymous · 1⤊ 1⤋