Distance = rate x time
The train travels a distance of 130 km and the plane travels a distance of 364 km.
Let the rate of the train = x. Then, the rate of the plane is 3x - 10. Let the time for both = t. We have the following equations:
130 = xt
364 = (3x - 10)(t)
Solve the first equation for t, which gives us: t = 130/x. Now, plug this into the second equation.
364 = (3x - 10)(130/x)
364 = 390 - 1300/x
-26 = -1300/x To make it easier to see, I'll re-write this as:
-26/1 = -1300/x We can always make any whole number a fraction by placing it over 1. Now, cross-multiply.
-26x = -1300
x = 50
The speed of the train is 50 km/h, so the plane's speed is 3x - 10 = 3(50) - 10 = 150 - 10 = 140 km/h
