SOLUTION: Two trains made the same 360-mile run. Since one train traveled 10 mph faster than the other, it arrived 3 hours earlier. Find the speed of each train.

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Question 1167193: Two trains made the same 360-mile run. Since one train traveled 10 mph faster than the other, it arrived 3 hours earlier. Find the speed of each train.
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

The time equation is


     -  = 3  hours.


where "r" is the rate of the slower train.


Answer  which can be guessed mentally is 30 mph.


Alternatively, you can reduce this equation to a quadratic equation and solve it by any method.


First step in this way is to multiply all the terms by r*(r+10) and simplify.


CHECK.   -  = 12 - 9 = 3 hours.



Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
slower train took 360/x hours where x is the speed
faster train took 360/(x+10) hours, where x+10 is its speed
faster train hours+3 is the slower train hours
so (360/x)-3=(360/(x+10)=(360-3x)/x
cross-multiply.
360x=360x+3600-3x^2-30x
so 3x^2+30x-3600=0
or x^2+10x-1200=0
(x+40)(x-30)=0
positive root is x=30 mph slower train, and it took 12 hours
x+10=40 mph for faster train, which took 9 hours.
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