Question

Two planes leave an airport at the same time, one traveling east at 250 miles/hr and the other traveling southwest at 300 miles/hr. How far apart are they after 3 hours?

Answer 1

They would be 1525.48 miles apart.

Explanation:

Given,

Speed of first plane = 250 miles/hr,

∵ Distance = speed × time,

So, the distance covered by the plane after 3 hours = 250 × 3 = 750 miles,

Similarly, speed of second plane = 300 miles/hr,

Distance covered by the plane after 3 hours = 300 × 3 = 900 miles,

Now, first plane is going east direction while other one is going towards southwest direction,

That is, the angle between them = 90° + 45° = 135°,

if x be the distance between them after 3 hours,

Using cosine law,

`x^2 = 750^2 + 900^2 - 2* 750* 900* \cos 135^(\circ)`

`x^2 = 562500 + 810000 - 1350000\cos 135^(\circ)`

`x^2 = 2327094.1546`

`\implies x = √(2327094.1546)\approx 1525.48`

Hence, they would be 1525.48 miles apart after 3 hours.