SOLUTION: Two trains, one going from Boston to New York and the other going from New York to Boston, started their trips at exactly same time. Speed of the first train was 10 miles per hour

Question 1073328: Two trains, one going from Boston to New York and the other going from New York to Boston, started their trips at exactly same time. Speed of the first train was 10 miles per hour less than twice the speed of the second train. How far from Boston station have they met in two hours, if the total distance between the cities along the rail road is 220 miles?
Found 3 solutions by josmiceli, josgarithmetic, MathTherapy:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
The wording is awkward.
" How far from Boston station have they met in two hours "
It's ungrammatical, but it sounds like they meet in 2 hrs
If this is true, then:
-------------------------
Let = the speed of the BOS - NY train in mi/hr
Let = distance in miles from Boston station when they meet
= distance from NY station when they meet
-------------------------------------------------------------
BOS - NY train:
(1)
NY - BOS train:
(2)
----------------------------
By substitution:
(2)
(2)
(2)
(2)
and

-----------------------------
(1)
(1)
(1)
The trains meet 140 mi from the Boston Station
---------------------------------------------
check:
(2)
(2)
and

OK

Answer by josgarithmetic(39625)   (Show Source): You can put this solution on YOUR website!
r, the speed of the train going from New York to Boston

SPEED TIME DISTANCE Boston to NY 2r-10 2 2(2r-10) NY to Boston r 2 2r Total 220

The only unknown is r. Distance summation gives , and solving this gives .

To find how far from Boston the two trains meet, simply use

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

Two trains, one going from Boston to New York and the other going from New York to Boston, started their trips at exactly same time. Speed of the first train was 10 miles per hour less than twice the speed of the second train. How far from Boston station have they met in two hours, if the total distance between the cities along the rail road is 220 miles?

Let distance from Boston station that they met, be D
Then speed of the Boston to New York train is:
Speed of the New York to Boston train is:
We then get the following SPEED equation:

D = 420 - 2D ------ Multiplying by LCD, 2
D + 2D = 420
3D = 420
D, or distance from Boston station that they met =
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