Answer:
a). 170 miles
b). Planes will be 500 miles apart after 1.1 hours.
Step-by-step 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 [tex]\frac{1}{3}[/tex] hours.
From the figure attached,
In right angle triangle DEC,
DE = 80 miles
BE = (Speed × duration) = [tex]300\times \frac{1}{3}=100[/tex] miles
Similarly, BC = [tex]150\times \frac{1}{3}=50[/tex] 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.
