Question 227721
The speed of train A is 12 km/hr is slower than the speed of train B. Train A travels 230 km in the same time it takes train B to travel 290 km,. Find the speed of each.


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


Step 2.  Let x be the speed of train B


Step 3.  Let x-12 be the speed of train A since it is 12 km/hr slower.


Step 4.  Let {{{time=distance/speed=230/(x-12)}}} be the time traveled by train A.


Step 5.  Let {{{time=distance/speed=290/x}}} be the time traveled by train B.


Step 6.  Set the equations in Steps 4 and 6 since they traveled at the same time.


{{{230/(x-12)=290/x}}}


Multiply by {{{x(x-12)}}} to both sides of the equation to get rid of the denominators.


{{{x(x-12)*(230/(x-12))=x(x-12)*(290/x)}}}


{{{230x=290(x-12)}}}


{{{230x=290x-290*12}}}


{{{230x=290x-3480}}}


Add 3480-230x to both sides of the equation



{{{230x+3480-230x=290x-3480+34080-230x}}}


{{{3480=60x}}}


Divide by 60 to both sides of the equation


{{{3480/60=60x/60}}}


{{{x=58}}} speed of  Train B and {{{x-12=46}} speed of Train A.


Check if times:  {{{230/46=290/58=5}}} hours which is a true statement.


Step 7.  ANSWER:  The speed of Train A is 46 km/hr and speed of Train B is 58 km/hr.


I hope the above steps were helpful.


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Respectfully,
Dr J

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