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 to close the gap?

If opposite directions, add rates. Their combined or "relative" rate is (40 + 60) = 100 mph.

Time 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

\(\frac{7}{10} hr * 40mph = 28 miles\)Answer B

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