Question

At noon a small plane left an airport and flew due east at 200 km/h. Two hours later another plane left the same airport and flew due south at 400 km/h. At what time will the planes be exactly 800 km apart from one another?

Answer 1

`color(blue)("Both planes will be 800 km apart after " 3 hrs 12 min " or at "15 hrs 12 min " or " 3 : 12 p.m.`

Explanation:

Let x be the time in hours taken for the planes be 800 km apart.

`"First plane would have travelled " (200 * x) km " in x hours."`

`"Second plane would have travelled " (400 * (x-2)) km " after x hours as it had started 2 hours behind."`

Since first plane has left towards east and the second towards south, they moved in perpendicular directions and we can conveniently apply Pythagoras Theorem.

`(200 * x)^2 + (400 * (x-2))^2 = 800^2`

`200^2 * (x^2 + (2(x-2))^2) = 800^2`

`x^2 + 4x^2 - 16x + 16 = (800/200)^2 = 16`

`5x^2 - 16x +cancel16 - cancel16 = 0`

`5cancel(x^2)^color(red)(x) = 16 cancelx`

`5x = 16 " or " x = 3.2 hours = 3 hrs 12 min`#