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Math Help - Walking Rates

  1. #1
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    Walking Rates

    Two children, who are 224 meters apart, start walking toward each other at the same instant at rates of 1.5m/sec. and 2m/sec, respectively a) when will they meet? b) how far will each have walked?

    At 6a.m. a snowplow traveling at a constant speed begins to clear a highway leading out of town. At 8a.m. an automobile begins traveling the highway at a speed of 30 mi/hr and reaches the plow 30 minutes later. Find the speed of the snow plow?

    A boy can row a boat at a constant rate of 5mi/hr in still water upstream. He rows upstream for 15 minutes and then rows downstream, returning to his starting point in another 12 minutes. a) Find the rate of the current. b) Find the total distance traveled.
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    Quote Originally Posted by amyl View Post
    Two children, who are 224 meters apart, start walking toward each other at the same instant at rates of 1.5m/sec. and 2m/sec, respectively a) when will they meet? b) how far will each have walked?

    [snip]
    Getting the time is the key.

    Pretend one child stays still and the other walks at 1.5 + 2 = 3.5 m/sec. How long to travel 224 meters?

    Now you have the time, stop pretending and get the distance each one walks.
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    Quote Originally Posted by amyl View Post
    [snip]
    At 6a.m. a snowplow traveling at a constant speed begins to clear a highway leading out of town. At 8a.m. an automobile begins traveling the highway at a speed of 30 mi/hr and reaches the plow 30 minutes later. Find the speed of the snow plow?
    [snip]
    Let speed of snowplow equal v and solve distance travelled by snowplow = distance travelled by car:

    2v + \frac{1}{2} v = \frac{1}{2} (30).
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    Quote Originally Posted by amyl View Post
    [snip]
    A boy can row a boat at a constant rate of 5mi/hr in still water upstream. He rows upstream for 15 minutes and then rows downstream, returning to his starting point in another 12 minutes. a) Find the rate of the current. b) Find the total distance traveled.
    The key is to get, v, the speed of current:

    Solve distance upstream = distance downstream, that is, solve

    (5 - v) \frac{1}{4} = (5 + v) \frac{1}{5}.
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