SOLUTION: Two trains are 440 miles apart, and their speeds differ by 12 mph. Find the speed of each train if they are traveling toward each other and will meet in 4 hours. Thank you

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Question 976403: Two trains are 440 miles apart, and their speeds differ by 12 mph. Find the speed of each train if they are traveling toward each other and will meet in 4 hours.
Thank you
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website!
Let one of the trains have the speed of r.
RT=D is how rate, time, distance are related for uniform travel rates.

__________________rate___________time_________distance
__________________r______________4_____________(____)
__________________r+12___________4_____________(____)
Total__________________________________________440

Fill the missing cells, form the necessary equation, and solve.

Answer by ikleyn(52794) (Show Source):
You can put this solution on YOUR website!

Let x be the speed of faster train (mi/h), and y be the speed of the other train (mi/h). Then you have the system of two linear equations in two unknowns

= = ,
= .

To solve the system, first add both equations. You will get

= = .

Hence, = = .

Now, substitute the found value of x into the first equation. You will get

= .

Hence, = = .

Answer. The speed of the faster train is 61 . The speed of the other train is 49 .