... 90km/h faster than the other. the two planes are 11,074km apart after 7 hours, what is the rate of each plane?
Answers (1)
We need to find the speed of the slower plane (x) and the faster plane (y).
The relative speed of the two planes is the total distance over the total time: 11,074 km per 7hr; or, 1,582km per 1hr.
11074 / 7 = 1582 / 1
The relative speed is equal to the speed of the slower plane (x), plus the speed of the faster plane (y).
x + y = 1582
The speed of the faster plane is equal to the speed of the slower plane, plus 90km/hr.
y = x + 90
x + y = 1582
x + (x + 90) = 1582
2x + 90 = 1582
2x = 1582 - 90
2x = 1492
2x / 2 = 1492 / 2
x = 746
The speed of the slower plane is 746km/hr, and the faster plane is traveling 90km/hr faster than that.
y = x + 90
y = 746 + 90
y = 836
The speed of the faster plane is 836km/hr.
To check, we can multiply the sum of both speeds by the amount of time (7hr).
7 * (746 + 836)
= 7 * 1582
= 11074 The given distance.