Question

Two planes flying opposite directions (north and south) pass each other 80 miles apart at the same altitude. The northbound plane is flying 300 mph (miles per hour) and the southbound plane is flying 150 mph. How far apart are the planes in 20 minutes? (Round your answer to one decimal place.) mi When are the planes 500 miles apart? (Round your answer to one decimal place.)

Answer 1

a). 170 miles

b). Planes will be 500 miles apart after 1.1 hours.

Explanation:

a). Two planes heading towards North and South when passed each other were 80 miles apart.

Distance between these planes after 20 minutes or
`(1)/(3)` hours.

From the figure attached,

In right angle triangle DEC,

DE = 80 miles

BE = (Speed × duration) =
`300* (1)/(3)=100` miles

Similarly, BC =
`150* (1)/(3)=50` miles

By Pythagoras theorem,

DC² = EC² + DE²

= (EB + BC)² + DE²

= (100 + 50)² + (80)²

= 28900

DC = √28900 = 170 miles

b). Now we have to evaluate the duration after which distance between the planes is 500 miles.

Let after t hours planes will be 500 miles apart.

Then EB = 300t

BC = 150t

Therefore, EC = EB + BC = 450t

It's given that DC = 500 miles

By Pythagoras theorem again,

DC² = EC²+ DE²

(500)²= (450t)²+ (80)²

250000 = 202500t² + 6400

2500 = 2025t² + 64

2025t² = 2436

t² = 1.20297

t = 1.097 hours ≈ 1.1 hours

Therefore, both the planes will be 500 miles apart after 1.1 hours.