algebra

for a question like: car A was traveling at 25miles/hour for 3 hours. Car B was traveling at 30mph for 6 hours. When will they meet?

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  1. wouldn't it depend on the starting points, ie, how far apart.

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  2. distance = rate * time
    One way is to make a table and fill it in. The same approach works for doing mixture problems. Your example does not work as you made it up because if they both start together car B will always be ahead.
    Let me change your example as follows:
    Car A and Car B are 100 miles apart and start toward each other.
    Car A goes 20 mph
    Car B goes 30 mph
    where and when do they meet?
    car # rate time distance
    A______20__*__t___=___20 t
    B______30__*__t___=___30 t

    Now since the total distance they rolled was 100 miles you can see that
    20 t + 30 t = 100
    so
    50 t = 100
    t = 2 hours
    and car A went 20*2 = 40 miles
    and car B went 30*2 = 60 miles

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  3. Now to make it harder, keep everything the same but say car B starts 1/2 hour later than car A. Then:
    car #_ rate __time_____ distance
    A______20__*____t_____=___20 t
    B______30__*_(t-.5)___=___30 (t-.5)

    Now 20 t + 30(t-.5) = 100
    20 t + 30 t - 15 = 100
    50 t = 115
    t = 2.3 hours for Car A
    Now our chart is:
    car #_ rate __time_______ distance
    A______20__*____2.3_____=___46 miles
    B______30__*(2.3-.5)=1.8=___54 miles

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