Math question

Question

a train travels 180km in the same time that a plane covers 450km. If the speed of the plane is 40km per hour less than 3 times the speed of the train, find both speeds?

Answer 1

v = speed of train

 

w = speed of plane

 

Given:  w = 3v - 40

 

t = time (same for both train and plane)

 

vt = 180 

 

wt = 450

 

Combine all the above and get a system of two equations in two unknowns v and t:

vt = 180

(3v - 40)t = 450

 

The top equation gives t = 180/v.  Substitute this into the bottom equation and solve for v:

 

(3v - 40)(180/v) = 450

540 - 7200/v = 450

7200/v = 90

 

v = 7200/90 = 80 km/hr

w = 3v - 40 = 3(80) - 40 = 200 km/hr

 

You can also find t:

 

t = 180/v = 180/80 = 2.25 hrs

 

Go ahead and test the solutions.