SOLUTION: A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 12 miles per hour faster than the southbou

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Question 1127685: A northbound train and a southbound train meet each other on parallel tracks heading in opposite directions. The northbound train travels 12 miles per hour faster than the southbound train. After 1.5 hours, they are 177 miles apart. At what speeds are the two trains traveling
Found 3 solutions by ikleyn, addingup, greenestamps:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
Let x be the speed of the slower speed train, in miles per hour.

Then the speed of the faster train is  (x+12) mph.


In 1.5 hours, the slower train covered the distance of 1.5*x miles,

while the faster train covered the distance of 1.5*(x+12) miles.


Since they travel in opposite directions, the full distance between them is the sum of partial distances.


    1.5x + 1.5*(x+12) = 177.


    1.5x + 1.5x + 18 = 177


    3x = 177 - 18 = 159  ====>  x = 159/3 = 53.


Answer.  The trains travel at 53 and 65 miles per hour.

Solved.

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Answer by addingup(3677)   (Show Source): You can put this solution on YOUR website!
NB train = SB + 12
After 1.5 hrs they are 177 miles apart.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Let the speed of the SB train be x. Then, the speed of the NB train is x + 12:
x + x + 12 = 2x + 12 This is the speed at which they are driving away from one another. And they do this for 1.5 hours:
1.5(2x + 12) = 177
3x + 18 = 177
3x = 159
x = 53 this is the speed of the southbound train.
The NB train is going 12 miles faster:
53 + 12 = 65 this is the speed of the NB train.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:
1.5(53 + 65) = 177
79.5 + 97.5 = 177 Correct

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The distance between the two trains is increasing at a rate of 177 miles in 1.5 hours, which is 177/1.5 = 118 miles per hour.

That 118 miles per hour is the sum of the speeds of the two trains. Since one train is traveling 12mph faster than the other, we can call the two speeds x and x+12. Then





ANSWER: The two speeds are x = 53mph and x+12 = 65 mph.
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