word problem help!!?

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?


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

i got 100 miles which is wrong. would u plz explain how u got the right answer? thank u

Answer 1

First, figure out where the two planes will be at 3:00. They have flown for two hours, so plane A is 2*150 = 300 miles north and plane B is 2*200 = 400 miles west.

The distance between them is the hypotenuse of a right triangle (because north and west are at right angles) with the two sides having the lengths that we just calculated. Conveniently, this is a 3-4-5 triangle, so you can immediately say that the answer is 500 miles. But to do it the long way you would calculate the length of the hypotenuse as sqrt(300^2 + 400^2) = sqrt(90000 + 160000) = sqrt(250000) = 500

Answer 2

for one travels directly north at 150 mph:at 3PM,2hrs later it will be 150*2=300 miles north
for one that travels directly west at 200 mph,2 hrs later it will be 200*2=400 miles due west.
(make a small drawing of where they are from their starting position to be able to see this clearly)
so the distance apart will be the hypotenus of the right angled triangle( with the other
2 sides being 400 and 300).so the hypotenus will be 500.so the answer is 500 miles

Answer 3

well, the planes make a right angle flying at those headings, so u can imagine a right triangle with the distance between them being the hypotenuse. since theyre flying for 2 hours, u have to multiply their speeds by 2, this gives you the length of the 2 sides.(300 and 400 miles) so now u can use the pythagorean theorem to find the length of the hypotenuse. 300 squared + 400 squared=250000. the square root of 250000 is 500. your answer should be 500 miles

Answer 4

North plane travels 300miles
West plane travels 400 miles
These distances form two sides at right angles to each other in a right angled triangle.
By Pythagoras the third side is 500 miles.
The planes will be 500 miles apart.

Answer 5

The answer is 500 miles.
Distance covered by plane1 = 150mph x 2hrs
= 300 miles
Distance covered by plane2 = 200mph x 2hrs
= 400 miles
The lines joining the starting point, and the ending points of both the planes form a right angled triangle,
So, by Pythagoras Theorum,
Distance between them = root of( 300^2 + 400^2)
= root of 2500
= 500 miles..

Answer 6

3-1=2 hours
North
150*2=300 miles

west
200*2=400 miles.
The distance is the length of the hypotenuse
Remember triangle 3,4,5
Hence 500 miles.

That is
d^2=300*300+400*400
d=500

Answer 7

500 miles.
use Pythagorean Theorem.