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Math Help - 3 remaining word problems. Algebra 1

  1. #1
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    3 remaining word problems. Algebra 1

    Okay.. after getting a big packet at the start of the semester, I'm down to 3 problems out of 279 that I have no clue how to do. Please help, I want to know what I'm doing wrong with these equations, so if you can please posts step by step work with explanations.

    Problem One:
    Suppose you are flying an ultra-light aircraft. You fly to a nearby tonw, 18 miles away. With a tail wind, the trip takes 1/3 hour. Your return flight with head wind takes 3/5 hour.
    A. Find the average airspeed of the ultra-light aircraft
    B. Find the average wind speed.

    Problem Two:
    A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank.
    A. Write an equation for the rate of the canoe downstream.
    B. Write an equation for the rate of the canoe upstream.
    C. Solve the system to find the family's paddling speed in still water.
    D. Find the speed of the current of the river

    Problem Three:
    John Flies from Atlanta, Georgia, to San Francisco, California. It takes 5.6 hours to travel 2100 miles against the head wind. At the same time, Debby flies from San Francisco to Atlanta. Her plane travels with the same average airspeed, but with a tail wind, her flight takes only 4.8 hours.
    A. Write a system of equations that reltaes time, airspeed, and wind speed to distance for each traveler.
    B. Solve the system to find the airspeed.
    C. Find the wind speed.

    -----

    Please help, I was absent when teach taught this, so I'm drawing up a blank with all my wrong equations.
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  2. #2
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    Quote Originally Posted by Auburn View Post
    Okay..

    Problem One:
    Suppose you are flying an ultra-light aircraft. You fly to a nearby tonw, 18 miles away. With a tail wind, the trip takes 1/3 hour. Your return flight with head wind takes 3/5 hour.
    A. Find the average airspeed of the ultra-light aircraft
    B. Find the average wind speed.

    ...
    I'm going to show you how to do the first question. The other questions have to be done similarly:

    Let denote v_a the speed of the air-plane through still air and v_w the speed of the wind.

    Speed of the air-plane and tail wind add up to the resulting speed; the difference between the speed of the air-plane and the head wind is the resulting speed on the return flight. Speed is defined by:

    speed=\dfrac{distance}{time}

    You'll get a system of simultaneous equations:

    \left|\begin{array}{l}v_a+v_w=\dfrac{18}{\frac13}=  54 \\v_a-v_w=\dfrac{18}{\frac35}=30 \end{array}\right.

    Solve for v_a and v_w. I've got v_a = 42~\vee~v_w= 12
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