math help asap

Question

a train travels 100 km in the same the plane covers 350km. If the speed of the plane is 20 km per less than 4 times the speed of the train, find both speeds.

 

Train speed?

 

planes speed?

Answer 1

Let x=speed of the train and y=speed of the pane.  Then we have

 

                        100/x = 350/y

                        y =4x-20

 

Substituting y=4x-20 into the top equation, we obtain

 

                          100/x = 350/(4x-20)

                          350x = 100(4x-20)

                          350x =400x - 2000

                          -50x = -2000

                          x = 40 km/hr

 

Then y=4(40)-20=140 km/hr.

 

Answer 2

Distance = rate x time

 

If the train has a speed of x, the the plane has a speed of (4x - 20)

 

The train travels 100 km and the plane travels 350 km in the same amount of time

 

Since the time is equal, we can solve the distance formula for time. Letting D = distance, r = rate, and t = time

 

D = r x t

 

t = D/r 

 

Since we know D and r for both the train and plane, we can set up the following

 

100/x = 350/(4x - 20)

 

Cross multiply 

 

100(4x - 20) = 350x 

 

400x - 2000 = 350x

 

50x - 2000 = 0

 

50x = 2000

 

x = 40

 

The train has a speed of 40 km/h, and the plane has a speed of 4x - 20 = 4 * 40 - 20 = 160 - 20 = 140 km/hr