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

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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) About Me  (Show Source):
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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 +s+%7D%7D+=+the+speed+of+NY+-+BOS+train+in+mi%2Fhr%0D%0A%7B%7B%7B+2s+-+10+ = the speed of the BOS - NY train in mi/hr
Let +d+ = distance in miles from Boston station when they meet
+220+-+d+ = distance from NY station when they meet
-------------------------------------------------------------
BOS - NY train:
(1) +d+=+%28+2s+-+10+%29%2A2+
NY - BOS train:
(2) +220+-+d+=+s%2A2+
----------------------------
By substitution:
(2) +220+-+%28+2s+-+10+%29%2A2+=+2s+
(2) +220+-+4s+%2B+20+=+2s+
(2) +6s+=+240+
(2) +s+=+40+
and
+2s+-+10+=+2%2A40+-+10+
+2s+-+10+=+70+
-----------------------------
(1) +d+=+%28+2s+-+10+%29%2A2+
(1) +d+=+70%2A2+
(1) +d+=+140+
The trains meet 140 mi from the Boston Station
---------------------------------------------
check:
(2) +220+-+d+=+s%2A2+
(2) +220+-+d+=+80+
and
+140+%2B+80+=+220+
OK

Answer by josgarithmetic(39625) About Me  (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 highlight_green%282%282r-10%29%2B2r=220%29, and solving this gives highlight_green%28r=40%29.

To find how far from Boston the two trains meet, simply use 220-2r
220-2%2A40
220-80
highlight%28140%29

Answer by MathTherapy(10555) About Me  (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: D%2F2

Speed of the New York to Boston train is: %28220+-+D%29%2F2

We then get the following SPEED equation: D%2F2+=+2%28%28220+-+D%29%2F2%29+-+10

D%2F2+=+220+-+D+-+10

D%2F2+=+210+-+D

D = 420 - 2D ------ Multiplying by LCD, 2

D + 2D = 420

3D = 420

D, or distance from Boston station that they met = highlight_green%28matrix%281%2C4%2C+420%2F3%2C+or%2C+140%2C+miles%29%29