Question 214693
A train travels 150 km in the same time that a plane covers 400 km. If the speed of the plane is 20 km per hr less than 3 times the speed of the train, find both speeds.


Step 1.  Let s be the speed of train and let p be the speed of the plane.


Step 2.  Speed = distance/time or time = distance/speed


Step 3.  150/s is the time traveled by the train and 400/p is the time traveled by the plane. Set the times of the train and plane to be equal as given.


{{{150/s=400/p}}}


{{{p=400s/150=8s/3}}}


Step 4.  p=3s-20   where the speed of the plane is 20 km per hr less than 3 times the speed of the train.


Step 5.  Substitute p in Step 3 into Step 4.


{{{p=3s-20}}}


{{{8s/3=3s-20}}}


Multiply 3 to both sides of the equation


{{{3*8s/3=3*(3s-20)}}}


{{{8s=9s-60}}}


Add 60-8s to both sides of equation


{{{8s+60-8s=9s-60+60-8s}}}


{{{60=s}}}


{{{p=8*60/3}}}


{{{p=160}}}


Step 6.  ANSWER:  The speed of the train is 60 km/hr and the speed of the plane is 160 km/hr.


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J