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Math Help - Quadratic Equation application with distance , rate , and time .

  1. #1
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    Quadratic Equation application with distance , rate , and time .

    Naoki bikes the 36 mi to Hillsboro averaging a certain speed. The return trip is made at a speed 3 mph slower. Total time for the round trip is 7 hr. Find Naoki's average speed on each part of the trip.

    I set up a table.

    Trip 1: Distance = 36 Speed = r Time = ???
    Trip 2: Distance = 36 Speed = r-3 Time = ???

    What do I set time as? x divided by 7?  \frac{X}{7} ?
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  2. #2
    MHF Contributor harish21's Avatar
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    for the first trip, if you suppose that he is travelling at a speed of x miles/hour and suppose that he takes t hours to complete the trip, then:
    x miles/hour * t hours = 36

    xt=36

    likewise for the second trip, his speed is (x-3) miles/hour and time is (7-t) hours...
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  3. #3
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    Quote Originally Posted by Kyrie View Post
    Naoki bikes the 36 mi to Hillsboro averaging a certain speed. The return trip is made at a speed 3 mph slower. Total time for the round trip is 7 hr. Find Naoki's average speed on each part of the trip.

    I set up a table.

    Trip 1: Distance = 36 Speed = r Time = ???
    Trip 2: Distance = 36 Speed = r-3 Time = ???

    What do I set time as? x divided by 7?  \frac{X}{7} ?
    The easiest way to figure out what you should set t as is by using the equation for average speed, r=  \frac{d}{t}. Solving for time multiply by t and then divide by speed so t=  \frac{d}{r}.

    Next Substitute in our given values for trip 1 and trip 2.
    Trip 1: t=  \frac{36}{r}
    Trip 2: t=  \frac{36}{r-3}

    Now since we are also given the time for a round trip is 7 hours, we can say Trip 1 + Trip 2= 7 hours,  t_{1} +  t_{2}.

     \frac{36}{r}+  \frac{36}{r-3}=7

    Now you can solve by multiplying by a least common divisor and solve for r to find the speed of the first trip and subtract 3 from that for Naoki's average speed on the return trip.
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