Question 224529
A train travels 120 km in the same time that a plane covers 336 km. If the speed of the the plane is 10 km per hour less than 3 times the speed of the train, find both speeds.


Step 1.  {{{distance = speed * time}}} and {{{speed = distance/time}}}


Step 2.  Let {{{120/t}}} be the speed of the train where t is the time traveled in 120 km.


Step 3.  Let {{{336/t}}} be the speed of the plane traveled in 336 km with the same time t.


Step 4.  Then {{{336/t=3*120/t-10}}} since the speed of the the plane is 10 km per hour less than 3 times the speed of the train, 


Step 5.  Multiply by t to both sides of the equation.


{{{t*336/t=t*3*120/t-t*10}}}


{{{336=360-10t}}}


Add 10t-336


{{{336+10t-336=360-10t+10t-336}}}


{{{10t=24}}}


Divide 10 to both sides of the equation


{{{10t/10=24/10}}}


{{{t=2.4}}}  Then {{{120/2.4=50}}} and {{{336/2.4=140}}}


Also, note that the plane's speed is 10km/hour less than 3 times the speed of the train.


Step 6.  ANSWER:  The speed of the train is 50 km/hr and the plane's speed is 140 km/hr.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J