Question 194472
Ok the problem asks us to find the rate or speed of each plane. First lets set up some variables for the speed of each plane.
Lets call the 1st plane speed "a" and the 2nd plane speed "b"
speed of 1st plane = a
speed of 2nd plane = b
We are told that the 1st plane is flying 25mph slower than the 2nd plane
So the speed of the 1st plane = speed of 2nd plane minus 25mph
a = b - 25
Ok so we have one equation to work with, but since there are two variables to solve for we need another equation.
The next part of the problem tells us that after 2 hours of flying the planes are 470 miles apart. So 2 hours times the speed of the first plane plus 2 hours times the speed of the second plane equals a distance of 470 miles.
2a + 2b = 470
Now we have a system of equations that we can use to solve for the variables a and b
So since we have shown that a = b - 25 we can substitute (b - 25) for a in the second equation and solve for b
2a + 2b = 470
2(b - 25) + 2b = 470  '' replace a with (b - 25) ''
2b - 50 + 2b = 470  '' multiply 2 times b and 2 times -25 ''
4b - 50 = 470 '' combine 2b + 2b ''
4b = 520 '' add 50 to both sides ''
b = 130 '' divide 4 into both sides ''
So the speed of the second plane is 130 mph
And since a = b - 25
The speed of the first plane is 105 mph