SOLUTION: The speed of a plane is 5 times as great as the speed of a scooter. The scooter takes 6 hours longer than the plane to travel 600km. Set up the rational expression using distance,

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Question 1191110: The speed of a plane is 5 times as great as the speed of a scooter. The scooter takes 6 hours longer than the plane to travel 600km. Set up the rational expression using distance, speed and time chart and then solve the equation what is the speed of the plane. Find the speed and time for both
Answer by ikleyn(52818) About Me  (Show Source):
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The speed of a plane is 5 times as great as the speed of a scooter.
The scooter takes 6 hours longer than the plane to travel 600km.
Set up the rational expression using distance, speed and time chart
and then solve the equation what is the speed of the plane.
Find the speed and time for both
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Let x be the speed of the scooter, in km/h.

Then the speed of the plane is 5x km/h.


The time for the scooter to travel 600 km is  600%2Fx  hours.

The time for the plane   to travel 600 km is  600%2F%285x%29  hours.


The difference of these amounts of time is 6 hours.

So we write this "time" equation

    600%2Fx - 600%2F%285x%29 = 6 hours.


Thus the setup is complete.


To solve the equation, multiply both sides by 5x.  You will get then

    3000 - 600 = 6*(5x),

or

       2400    = 30x

          x    = 2400/30 = 80.


ANSWER.  The speed of the scooter is  80 km/h.  The speed of the plane is 5*80 = 40 km/h.

Solved.