Question 422865
The distance each plane travels will be given by its speed multiplied by the time until impact.
So we have d1 = v1*t and d2 = v2*t, for planes 1 and 2
We know that the total distance d = d1 + d2, and v2 = v1 + 120
So the system of equations is:
1) d1 = v1*t
2) d2 = (v1 + 120)*t
3) d1 + d2 = 1500
Adding 1) and 2) gives d1 + d2 = v1*t + (v1 + 120)*t
Equating the above equation to the RHS of 3) gives v1*t + (v1 + 120)*t = 1500
Since t = 1.5 h, we have one unknown and we can solve for v1:
1.5*v1 + 1.5*v1 + 180 = 1500 -> v1 = (1500-180)/3 = 440 mph
So the speed of the other plane is v2 = 440 + 120 = 560 mph
Check: 440 mph * 1.5 h + 560 mph * 1.5 h = 660 + 840 = 1500 miles