saswata4s wrote:
two trains face each other 100 miles apart on two parallel tracks. Train B starts moving towards train A at 60 miles/hr. Half an hour later, train A starts moving towards train B at 40 miles/hr. How many miles will train A travel before it passes train B?
(a) 25
(b) 28
(c) 33
(d) 35
(e) 40
Sometimes these questions are called "crash" or "kiss"; distance between is the "gap." A and B move in opposite directions toward one another and will meet.
How far A travels depends on:
-- How far B went alone; and
-- Time for both trains, with both moving, to close the gap
1) Adjust gap distance. B moved alone for a time. Beginning distance = 100 miles
B travels toward A.
\(rt=D\). B covers
\((60mph*\frac{1}{2}hr)=
30\) miles before A moves. Distance gap is shortened: (100-30) = 70 mi
2) How long (time needed) to close the gap?
We need the combined rate to find the time that both traveled
If opposite directions,
add the rates. Their combined or "relative" rate is (40 + 60) = 100 mph.
Time that both traveled to close the gap:
\(\frac{Distance}{rate}= time =\frac{70}{100}=\frac{7}{10}hr\)3) Miles train A will travel before it passes train B? A's travel distance depends only on the shortened gap. So
\(r_{A}*t=D_{A}\)
\(40mph *\frac{7}{10} hr= 28 miles\)Answer B
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