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Math Help - "Mixture" and "Distance, Speed, and Time" Word Problems

  1. #1
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    "Mixture" and "Distance, Speed, and Time" Word Problems

    Hello,

    I have three algebra word problems that I have literally spent hours working on, and I feel extremely stupid because I cannot figure out how to set them up to get the correct answer! Any help would be greatly appreciated!

    Here goes:

    1. A radiator in a car - with a capacity of 3.7 liters - is filled with a solution of 60% antifreeze and 40% water. How much coolant should be drained and replaced with water to reduce the antifreeze concentration to 50%?

    2. A pilot flew a jet from Montreal to Los Angeles, a distance of 2500 miles. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 9 hours and 10 minutes. What was the speed from Montreal to Los Angeles?

    3. A salesman drives from Ajax to Barrington, a distance of 120 miles, at a steady speed. He then increases his speed by 10 mph to drive the 150 miles from Barrington to Collins. If the second leg of his trip took 6 minutes more than the first leg, how fast was he driving between Ajax and Barrington?

    Thanks in advance!
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  2. #2
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    Re: "Mixture" and "Distance, Speed, and Time" Word Problems

    Find something that you can track.

    Radiator

    1: 3.7 litre * 0.60 = Amount of Coolant at the start.
    2: We'll be draining x litre, and that's x litre * 0.60 of coolant.
    3: We'll be adding x litre of water. That's x litre * 0 = 0 litre coolant.
    4: W need to end up with 3.7 litre * 0.50 total coolant

    Then 3.7*0.6 - x*0.6 + x*0.0 = 3.7*0.50

    If you would prefer to equate the water, you may. It is very nearly the same

    Then 3.7*0.4 - x*0.4 + x*1.0 = 3.7*0.50

    Sometimes one or the other is a little easier. The one with the zero (0) usually wins that contest.

    Solve both and convince yourself.
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  3. #3
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    Re: "Mixture" and "Distance, Speed, and Time" Word Problems

    Hello, aspiringphysician!


    2. A pilot flew a jet from Montreal to Los Angeles, a distance of 2500 miles.
    On the return trip, the average speed was 20% faster than the outbound speed.
    The round-trip took 9 hours and 10 minutes.
    What was the speed from Montreal to Los Angeles?

    Let x = outbound speed.
    Then 1.2x = return speed.

    He flew 2500 miles outbound at x mph.
    . . This took \tfrac{2500}{x} hours.

    He flew 2500 mile back at 1.2x mph.
    . . This took \tfrac{2500}{1.2x} hours.

    \text{The total time was: }\:\text{9 hours, 10 minutes} \,=\,9\tfrac{1}{6}\text{ hours} \,=\,\tfrac{55}{6} hours.

    There is our equation . . . . \dfrac{2500}{x} + \dfrac{2500}{1.2x} \;=\;\dfrac{55}{6}

    . . . Go for it!
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  4. #4
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    Re: "Mixture" and "Distance, Speed, and Time" Word Problems

    Sorry...I've been busy lately...thanks so much for your help!!!!!
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