07/05/2013
Answer to the Uniform Motion Problem on Jun 22:
Let E be the distance Emily runs and M be the distance Mandy runs until they meet again.
By the equation of Distance (D=tS) where t=time and S=speed, we can write the 2 equations for Emily and Mandy as:
1. E=9t
2. M=7t
The total distance they run until meeting (in opposite direction) is 400m, therefore E+M=400; or M=400-E
Substitute "M" into equation 2 above we get 400-E=7t, then rearrange the terms to get E=400-7t, since E=9t as stated in equation 1 above, therefore 400-7t=9t, solve this 1 variable equation by combining like terms: 400=9t+7t or 400=16t; therefore t=25.
Substitute "t" into 1: E=9(25) = 225
Substitute "t" into 2: M=7(25) = 175
Hence, they will meet again after 25sec and Emily has run 225m (Mandy 175m).