SOLUTION: Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 75 /kmh slower than the other. If the two planes are 6892km apart afte

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels 75 /kmh slower than the other. If the two planes are 6892km apart afte      Log On


   



Question 905927: Two airplanes leave an airport at the same time and travel in opposite directions. One plane travels
75
/kmh
slower than the other. If the two planes are
6892km
apart after
4
hours, what is the rate of each plane?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = the distance in km the faster plane travels in km
+6892+-+d+ = the distance the slower plane travels in km
Let +s+ = the speed of the faster plane in km/hr
+s+-+75+ = the speed of the slower plane in km/hr
----------------------------------------
Equation for faster plane:
(1) +d+=+s%2A4+
Equation for slower plane:
(2) +6892+-+d+=+%28+s+-+75+%29%2A4+
--------------------------
Substitute (1) into (2)
(2) +6892+-+4s+=+%28+s+-+75+%29%2A4+
(2) +6892+-+4s+=+4s+-+300+
(2) +8s+=+7192+
(2) +s+=+899+
and
+s+-+75+=+824+
-----------------
The speed of the faster plane is 899 km/hr
The speed of the slower plane is 824 km/hr
check:
(2) +6892+-+d+=+%28+s+-+75+%29%2A4+
(2) +6892+-+d+=+824%2A4+
(2) +d+=+6892+-+3296+
(2) +d+=+3596+
and
(1) +d+=+s%2A4+
(1) +d+=+899%2A4+
(1) +d+=+3596+
OK