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Math Help - Average Speed Question

  1. #1
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    Average Speed Question

    Hi, I am having trouble getting started on this physics problem...it seems fairly simple just need some hints:

    You drive on Interstate 10 from San Antonio to Houston, half the time at 73 km/h and the other half at 90 km/h. On the way back you travel half the distance at 73 km/h and the other half at 90 km/h. What is your average speed a) from San Antonio to Houston, b) from Houston back to San Antonio, and (c) for the entire trip?

    I know average speed is the total distance during the trip divided by the total time for the trip but I am not sure how to determine those.

    Thanks.
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  2. #2
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    Hello, mmattson07!

    This was trickier than I thought . . .


    You drive on Interstate 10 from San Antonio to Houston,
    half the time at 73 km/h and the other half at 90 km/h.

    On the way back you travel half the distance at 73 km/h and the other half at 90 km/h.

    (a)What is your average speed from San Antonio to Houston?
    For convenience, assume that the distance from San Antonio to Houston is 1314 km.


    We drove x km at 73 mph.
    . . This took: . \frac{x}{73} hours.

    We drove the other 1314-x km at 90 mph.
    . . This took: . \frac{1314-x}{90} hours.

    These two times are equal: . \frac{x}{73} \:=\:\frac{1314-x}{90} \quad\Rightarrow\quad x \:\approx\:588.48 km.


    We drove 588.48 km at 73 km/hr.
    . . This took: . \frac{588.48}{73} \:\approx\:8.06 hours

    We drove the other: . 1314 - 588.48 \,=\,725.52 km at 90 km/hr.
    . . This took: . \frac{725.52}{90} \;\approx\:8.06 hours. .(Of course!)

    We drove 1314 km in 16.12 hours.

    From San Antonio to Houston, we averaged: . \frac{1314}{16.12} \:\approx\:81.51 km/hr.




    (b) What is your average speed from Houston back to San Antonio?

    We drove 657 km at 73 km/hr,
    . . This took: . \frac{657}{73} \:=\:9 hours.

    We drove 657 km at 90 km.hr.
    . . This took: . \frac{657}{90} \:=\:7.3 hours.

    We drove 1314 km in 16.3 hours.

    From Houston to San Antonio, we averaged: . \frac{1314}{16.3} \:\approx\: 80.61 km/hr.




    (c) What is your average speed for the entire trip?

    We drove a total of 2628 km in a total of 32.42 hours.

    For the entire round trip, wel averaged: . \frac{2628}{32.42} \;\approx\;81.06 km/hr.

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