a train travels 150 km in the same time that a plane travels 400 km. if the rate of the plane is 20 km per hour less than three times the rate of the train, find both rates

Speed of train = 60 km/hr

Speed of plane = 160 km/hr

Explanation:

We can construct the following equations from the given information:

Speed of train * time = 150 - Equation 1

Speed of plane * time = 400 - Equation 2

Speed of plane = (3 * Speed of train) - 20 - Equation 3

We can solve these three simultaneous equations for the three variables (speed of train, speed of plane, time).

Substituting within Eq. 1 and Eq. 2 we get:

Speed of plane * 150 = 400 * Speed of train - Equation 4

Finally, solving Eq. 4 and Eq. 3 simultaneously we get:

Speed of train = 60 km/hr

Speed of plane = 160 km/hr