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Math Help - distance, speed and time problem/mixture and salary problems

  1. #1
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    distance, speed and time problem/mixture and salary problems

    help guys. i forgot how to do this, i forgot

    1. Two, cyclist, 90 mi apart, start riding toward each other at the same time. One cycles is twice as fast as the other. If they meet 2h later, at what average speed is each cyclist traveling?

    2. A pot contains 6L of brine at a concentration of 120g/L. How much of the water should be boiled off to increase the concentration of 200 g/L?

    3. Helen earns $7.50 an hour at her job, but if she works more than 35 hours in a week she paid 1 1/2 (one and one half) times her regular salary for the overtime hours worked. One week her gross pay was $ 352.50. How many overtime hours did she work that week?

    thanks for helping!
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  2. #2
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    1. Since one is cycling 2x faster than the other, they will meet at 60mi from one side of one starting point and 30mi from the other side of starting point. So one travels 15m/h and the other travels 30m/h

    Average speed is (15+30)/2 = 22.5m/h


    2. 6L of 120g/L brine has 720g of brine in it.

    So 720g / ? = 200g/L

    720g / 200g/L = 3.6L

    6L - 3.6L = 2.4L needs to be boiled off


    3. $7.50 * 35 = $262.50
    She has earned $262.50 for her non-overtime hours.

    Extra profit = $352.50 - $262.5 = $90.00

    One and a half times over the original profit = $11.25 an hour
    $90.00 / $11.25 = 8 overtime hours worked
    Last edited by DavidM; July 24th 2010 at 02:08 AM.
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  3. #3
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    thank you very much mr. David! you really helped me! thanks again!
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  4. #4
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    1) let x be the speed of the slower cyclist
    they together have ttravelled at distance of 90 miles
    therfore :
    2x+4x=90

    x=15

    the slower cyclist is travelling at 15 miles/hr
    while the faster cyclist is travlling twice as fast that is30 miles/hr

    2) c=\frac{m}{V}

    m= (c)(V)

    m= (120)(6)

    m=720g

    for c to be 200
    200 = \frac{720}{V}

    V=\frac{720}{200}

    V=3.6

    the new volume should be 3.6 L
    therfore
    6-3.6=2.4L

    2.4L should be evaporated

    3) let x= the number of hours worked overtime
    normal pay for 35 hrs is
    35x7.50=262.50

    262.50 + (1.5)(7.5)x=352.50

    x=8
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