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I an taking the SAT this week and I am so screwed. I keep getting these types(and ratio and probability- tips?) of questions wrong on practices. I basically set up a chart for d(distance/amount of sth), v(speed/rate), and t(time) and try to fill it out. I usually fill it out(except for #2) correctly, but I don't know what to do with the results LOL. Thank you(I feel so dumb right now), and I hope you can provide some tips and explanations, and also some good sites explaining the ratio, probability, and word problem sections.

1. A freight train left a station at 12 noon, going north at a rate of 50 miles per hour. At 1:00pm, a passenger train left the same station, going south at a rate of 60 miles per hour. At what time were the trains 380 miles apart?

2. A man drove to work at an avg rate of speed of 60 miles per hour and returned over the same route driving at an avg rate of speed of 40 miles per hour. If his total driving time was 1 hour, what was the total number of miles in the round trip?

3. If x people working together at the same rate can complete a job in h hours, what part of the same job can one person working alone complete in k hours?

  • Math -

    t is time after 12 noon

    f for freight train
    distance f = df = 50 t

    p for passenger train
    dp = 60 (t-1)

    when is dp - df = 300 ?

    60(t-1) - 50 t = 380
    10 t - 60 = 380
    10 t = 440
    t = 44 hours
    so one day and 20 hours
    so 8 am
    total distance = 2d
    drove out for time t
    drove back for time = 1-t
    d = 60 t
    d = 40 (1-t)
    60 t = 40 (1-t)
    100 t = 40
    t = .4 hour
    d = 60*.4 = 24 miles
    2d = 48 miles round trip
    one man works at 1/(xh) jobs / man hour
    so man hours per job = x h
    k/(x h) = fraction desired

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