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Question
1) A 100 meter long train moving at the speed of 30 meter per second crosses another 120 meter long train coming from opposite direction in 6 seconds. What is the speed of second train?

2) 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days.In how many days will 10 women complete it?

3) Excluding stoppages the speed of a bus is 54kmph and including stoppages,it is 45kmph. For how many minutes does the bus stop per hour?

Answer
The second train moves s meters per second. The distance between trains decreases by 30+s meters per second.

Consider points at the front and rear of each train. When the front points of the trains meet, the rear points are 100+120 = 220 meters apart. After another six seconds, the rear points meet.
220 meters 1 second/(30+s meters) = 6 seconds
220 = 6(30+s)
s = 20/3 = 6⅔ meters per second.
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"4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days."
(4m + 6w)8 = (3m + 7w)10
32m + 48w = 30m + 70w
m = 11w

3m + 7w = 33w + 7w = 40w
40 women can complete the job  in 10 days.
It takes 10 women 40 days to complete the work.
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"Excluding stoppages, the speed of a bus is 54kmph. Including stoppages, the average speed is 45kmph"
Let s be the number of minutes the bus is stopped per hour.
s minutes = (s/60) hours
1-(s/60) is the fraction of the hour the bus is moving.

(1-(s/60)) 54 km/hour = 54-0.9s km/hour
54-0.9s km/hour = 45 km/hour
9-0.9s = 0
s = 10 minutes
The bus is stopped for 10 minutes per hour.

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Janet Yang

Expertise

Word problems are my favorite type of math questions! I would not feel comfortable answering questions that require specialized knowledge (Physics, Statistics, etc.) because I have not studied these in depth.

Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language.

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley, and a Master of Business Administration degree from The Wharton School.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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