A commercial airplane flying with a speed of 700 mi/h is detected 1000 miles away with a radar. Half an hour later an interceptor plane flying with a speed of 800 mi/h is dispatched. How long will it take the interceptor plane to meet with the other plane? plz answer will mark as brainliest
Answers
Answer: 13.5 hours
Step-by-step explanation:
Speed of commercial airplane = 700 mi/h
It is 1000 miles away from the starting position.
Interceptor plane is dispatched half an hour later, whose speed = 800 mi/h
Thus, distance covered by the commercial airplane in 0.5 hrs = 700*0.5
= 350 miles
So, initial distance between the two airplanes = 1000 + 350 = 1350 miles
Now,
Distance covered by commercial airplane after 1 hour = 700 miles
And interceptor plane = 800 miles
Distance between the two planes after 1 hour = (700 + 1350) - 800
= 2050 - 800
= 1250 miles
Similarly,
Distance between the two planes after 2 hours = 1150 miles
Distance between them after 'n' hours = 0 miles
1250, 1150,.........., 0
This forms an A.P. with a = 1250 and d = -100.
Last term = l = 0
We need to find 'n'.
l = a + (n - 1)d
0 = 1250 + (n - 1)(-100)
n - 1 = -1250/-100 = 12.5
∴ n = 13.5
Thus, it will take 13.5 hours for the interceptor plane to meet with the other plane.
Hope it helps you.