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Math Help - Carlos and his Bike

  1. #1
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    Question Carlos and his Bike

    Please help with this story problem, I'm still recovering from summer math-deprivation, and I need a refresher!

    Carlos cycles for 2 hours at a fast speed, then cycles for three more hours at a speed 10 kph slower. If the entire distance traveled is 90 km, find Carlos' speed for the first two hours of travel.

    Thanks!
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  2. #2
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    Alright, here's what we know.

    He travels 2 hours at a fast speed, lets call that speed f km/h
    He then travels 3 hours at (f-10) km/h
    In these 5 hours, he travels 90km

    So we have the formula velocity = distance/time. If you don't know where that formula comes from, let me know and I'll explain.

    So we have:
    v = \frac{d}{t}
    d and t are given to us as 90 and 5 respectively
    v is going to be his average speed, so we take 2 times the fast speed plus 3 times the slower speed and divide it by 5. This gives us the average speed he travelled over the 5 hours.
    \frac{2f + 3(f-10)}{5} = \frac{90}{5}
    2f + 3f -30 = 90 by cancelling the 5's in the denominator and expanding 3(f-10)
    5f = 120
    f = 24 km/h

    So his faster speed is 24 km/h. Let me know if this solution did not make sense to you at any point.
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  3. #3
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    Perfect!

    That all made sense thanks so much for your help!
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