Question 1188398
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The other tutor has shown one good formal algebraic method for solving the problem.<br>
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.<br>
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.<br>
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.<br>
Megan runs 100m in 30 seconds and so takes 120 seconds to run 400m.<br>
Her brother runs 100m in 20 seconds and so takes 120 seconds to run 600m.<br>
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.<br>