I need help with this algebra question! Please show how you arrived at the solution. Thanks in advance!?

Question

If two planes leave the same airport at 1:00 PM, how many miles apart will they be at 3:00 PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?

I know that the answer is 500 miles, but how to I arrive at this solution?

50 miles
100 miles
500 miles
700 miles
1,000 miles

Answer 1

N (3pm)
|
| 300 miles
|
|__________________W(3pm)
(1pm) 400 miles

This is the graphical display of the question where the plane going north will have covered 300miles (150mph*2h) and other plane going west will have covered 400miles (200mph*2h).
So as North and West are perpendicular so to find distance between planes after 2 hours we have to measure the hypotenuse of the triangle with sides 300 and 400.
therefore by Pythagoras theorem we have distance= sqrt(300^2 + 400^2) = sqrt(250000)= 500 miles

Answer 2

In two hours the first plane will be 150*2 = 300 miles from the airport, while the second plane will be 200*2 = 400 miles from the airport. The planes are moving at a right angle to one another, so at 3:00 the two planes and the airport form the three vertices of a right triangle.

300^2 + 400^2 = x^2
900 + 1600 = x^2
2500 = x^2
500 = x

The two planes are 500 miles apart at 3:00.

Answer 3

Use the Pythagorean theorem.
A^2 + B^2 = C^2
A is the distance one plane traveled (150 mph for 2 hours = 300 miles)
B is the distance the other plane traveled (200 mph for 2 hours = 400 miles)
C is the distance apart
So 90000 + 160000 = C^2
C^2 = 250000
C = 500

Another way you could do it is to check the answers 50 is way to short, so is 100 (this would be the distance if the traveled in the same direction). 500 looks good, 700 is the distance if the traveled in opposite directions. 1000 is way to long. So 500 it is.

Answer 4

Plane A is going 150 mph, plane B is going 200 mph. Okay?

Plane A takes off at 1 PM and flies for two hours. 150+150=300. Plane A is 300 miles North.

Plane B takes off at 1 PM and flies for two hours. 200+200=400. 400 miles west.

The distance they're apart is what I believe is called the hypotneuse of the triangle. The distance going west is the bottom of the triangle, and the distance going north is the side. I don't remember my formulas for triangles, I'm sorry. But, I hope some of this could be of some help to you. Or it was just an insult to your intelligence if you already figured all that out.

Answer 5

One went 300 miles north in the two hours, and the other went 400 miles west. By the Pythagorean Theorem (a 3-4-5 triangle), they're 500 miles apart at 3 p.m.

Answer 6

Draw a straight vertical line and cross it with a straight horizontal line. Use 1 inch per 100 miles. Therefore, 2hrs at 150 miles per hour equals 3 inch up on the vertical line, and starting at the same point 2hrs at 200 miles per hour left on the horizontal line equals 4 inches. Now measure from the 3 inch mark Vertical to the 4 inch mark Horizontal and you get 5 inches. convert to 1 inch per 100 miles equals 500 miles.

Answer 7

since from 1pm to 3pm is 2 hours, just multiply the speed by 2

150 * 2 = 300
200 * 2 = 400

Now just use the pythagorean thereom

300^2 + 400^2 = c^2
90000 + 160000 = c^2
250000 = c^2
c = 500

ANS : 500

Answer 8

a) 14x^2 = 7x 14x^2 - 7x = 0 7x(2x-a million)=0 7x=0 2x-a million=0 x=0 x= a million/2 b) x ( x + 9 ) = 4 ( x + 6 ) x^2 + 9x = 4x + 24 x^2 +5x -24 = 0 (x+8) (x-3) = 0 x= -8 x=3 c) 2(x +a million )^2 - 3 = 5 (x + a million) 2(x^2+2x+a million) - 3 = 5x +5 2x^2 +4x +2 -3 = 5x +5 2x^2 - x -6 = 0 (2x +3) (x - 2) = 0 x= -3/2 x=2

Answer 9

the two airplanes' paths form two sides of a triangle. the distance between them is the hypotenuse.

formula for finding the length of the hypotenuse is pythagorean theorem: the hypotenuse squared = leg one squared + leg two squared.

so 300 squared + 400 squared = distance apart squared. take the square root, and you have your answer.

Answer 10

400 miles