SOLUTION: megan takes 30 seconds to run 100m while her brother takes 20 secs. if megan is given a 200 metre head start how long would it take her brother to catch up to her

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Question 1188398: megan takes 30 seconds to run 100m while her brother takes 20 secs. if megan is given a 200 metre head start how long would it take her brother to catch up to her
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
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megan takes 30 seconds to run 100m while her brother takes 20 secs.
if megan is given a 200 metre head start,
how long would it take her brother to catch up to her ?
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The Megan's rate running is  100%2F30 = 10%2F3  meters per second.


The brother's rate running is  100%2F20 = 5 meters per second.


Their rate approaching is the difference  5+-+10%2F3 = 15%2F3+-+10%2F3 = 5%2F3 m/s.


With headstart of 200 meters for Megan,  her brother will catch her in  200%2F%28%285%2F3%29%29 = 40*3 = 120 seconds. 


ANSWER.  The brother will catch Megan in 120 seconds.

Solved.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor has shown one good formal algebraic method for solving the problem.

While a formal algebraic solution was probably wanted, you can get some good mental exercise by solving the problem informally using logical reasoning and some relatively easy mental arithmetic.

For a fixed distance, the ratio of the times required by Megan and her brother are in the ratio 3:2. That means the ratio of their speeds is 2:3.

In this problem, they are running for the same amount of time, so Megan will run 2/3 as far as her brother. A bit of mental calculations show that if 2/3 as far as her brother is 200m less than her brother, then the distances the two of them run are 400m and 600m.

Megan runs 100m in 30 seconds and so takes 120 seconds to run 400m.

Her brother runs 100m in 20 seconds and so takes 120 seconds to run 600m.

So 120 seconds is the amount of time it takes her brother to catch up to her when she is given a 200m head start.