Two planes flying opposite directions (north and south) pass each other 80 miles apart at the same altitude. The northbound plane is flying 200 mph (miles per hour) and the southbound plane is flying 150 mph. When are the planes 200 miles apart? (Round your answer to one decimal place.)

Question

Two planes flying opposite directions (north and south) pass each other 80 miles apart at the same altitude. The northbound plane is flying 200 mph (miles per hour) and the southbound plane is flying 150 mph. When are the planes 200 miles apart? (Round your answer to one decimal place.)

Let after t hours planes will be 500 miles apart.

Then EB = 200t
BC = 150t
Therefore, EC = EB + BC = 350t
It's given that DC = 200 miles
By Pythagoras theorem again,
DC² = EC²+ DE²
(200)²= (350t)²+ (80)²
4000 = 122500t² + 6400
400 = 1225t² + 64
1225t² = 336
t² = 0.27438571
t=0.52 ≈ .52 hours = 31 mins
is the correct or did I do something wrong?

Answer 1

(350t)^2 + 80^2 = 500^2

Answer 2

Well, it seems like you did the math correctly! The planes will be 200 miles apart after approximately 31 minutes. However, I must say, those planes sure are good at keeping their distance. Maybe they're just really good at social distancing!

Answer 3

Your calculations appear to be correct. The time it takes for the planes to be 200 miles apart is approximately 0.52 hours or 31 minutes.

Answer 4

Two planes flying opposite directions (north and south) pass each other 80 miles apart at the same altitude. The northbound plane is flying 200 mph (miles per hour) and the southbound plane is flying 150 mph. When are the planes 200 miles apart? (Round your answer to one decimal place.)

(350t)^2 + 80^2 = 500^2

Well, it seems like you did the math correctly! The planes will be 200 miles apart after approximately 31 minutes. However, I must say, those planes sure are good at keeping their distance. Maybe they're just really good at social distancing!

Your calculations appear to be correct. The time it takes for the planes to be 200 miles apart is approximately 0.52 hours or 31 minutes.

Your calculation is correct! The planes will be 200 miles apart in approximately 31 minutes. Well done!