SOLUTION: The average speed of an airplane is four times as fast as the average speed of a passenger train. To travel 1440 km, the train requires 12h more than the airplane. Determine the av

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Question 1151457: The average speed of an airplane is four times as fast as the average speed of a passenger train. To travel 1440 km, the train requires 12h more than the airplane. Determine the average speeds of the train and the airplane.
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
                  SPEED      TIME            DISTANCE

AIRPLANE            4r        1440/(4r)         1440

TRAIN               r         1440/r            1440

Difference                     12

highlight_green%281440%2Fr-1440%2F%284r%29=12%29


1440%2Fr-360%2Fr=12
1080%2Fr=12
r=1080%2F12

r=90-----------the train
.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The average speed of an airplane is four times as fast as the average speed of a passenger train. To travel 1440 km, the train requires 12h more than the airplane. Determine the average speeds of the train and the airplane.
The train's speed is NOT 110 km/h, so IGNORE this from the other person: cross%28highlight%28r=110%29%29-----------the train

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let r be the average speed of the train, in kilometers per hour;

Then the average speed of the train is 4r,  according to the condition.


Time to travel 1440 km by train is  1440%2Fr  hours.


Time to travel 1440 km by airplane is  1440%2F%284r%29  hours.


The difference of times is 12 hours.  It gives you this "time" equation


    1440%2Fr - 1440%2F%284r%29 = 12  hours.     (1)


The second fraction in the left side is  360%2Fr, so this equation takes the form


    1440%2Fr - 360%2Fr = 12,   or

    1080%2Fr = 12.


Then  r = 1080%2F12 = 90.


ANSWER.  The average speed of the train is 90 km/h.

         The average speed of the airplane is 4 times 90 km/h,  or  360 km/h.


CHECK.  I will check equation (1).


        1440%2F80 - 1440%2F360 = 16 - 4 = 12 hours.   ! Precisely correct !

Solved.