Two trains depart from locations C and D, heading towards each other. The train from C leaves at 7 a.m. and arrives at D by 3 p.m., while the train from D departs at 9 a.m. and reaches C at 3 p.m. How long after 9 a.m. will the two trains encounter each other?

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Correct answer marked below

1 rac{5}{6} h

rac{12}{5} h

2 rac{1}{3} h

2 rac{2}{5} h

Correct

3 rac{1}{2} h

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Explanation

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Official Explanation

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The train from C starts at 7 a.m. and arrives at D at 3 p.m., taking a total of 8 hours. The train from D starts at 9 a.m. and reaches C at 3 p.m., taking 6 hours. The least common multiple (LCM) of 8 and 6 is 24. To find their speeds, we use the formula r * T = D. For train C: r * 8 = 24, which gives r = 3. For train D: r * 6 = 24, resulting in r = 4.…

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What this question tests

What it tests

Your application of distance = rate × time to trains, boats, and commuters, including relative speed.

Common trap

Mixing units (miles per hour vs. minutes) or averaging speeds — average speed is total distance over total time.