document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #819484 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The other tutor has shown one good formal algebraic method for solving the problem.

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "Megan runs 100m in 30 seconds and so takes 120 seconds to run 400m.

\n" ); document.write( "Her brother runs 100m in 20 seconds and so takes 120 seconds to run 600m.

\n" ); document.write( "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.

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