two planes departed simultaneously from parallel runways at

two planes departed simultaneously from parallel runways at an airport. they flew in the same direction. after 5 hours, the faster plane was 300 km ahead of the slower plane. find the distance flown by each plane if the total of these distances is 5 300 km.

Solution

Let x and y be the speeds ofthe planes.
In 5 hours,
The distance flown by the faster plane = 5x
The distance flown by the slower plane = 5y
Given, the distance between the planes
5x-5y = 300 ...(1)
Also, total distance flown by the planes
5x+5y = 5300 ...(2)
(1)+(2)=> 10x = 5600
x = 5600/10
x = 560 kmph
Substituting in (1), 5*560-5y = 300
-5y = 300-2800
-5y = -2500
y = (-2500)/(-5)
y = 500 kmph
The distance flown by the faster plane = 5*560 = 2800km
The distance flown by the slower plane = 5*500 = 2500km