Question 1210215
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Hi
Tim and Michelle drove from  A to B which was 285km away. Tim set off for  B at an average speed of 75km per hour.
48min later Michelle set off for B at a speed of 95km per hour. How long would Michelle take to catch up with Tim.
How far away was Tim from B when Michelle completed her journey 

Let time Michelle takes to catch up to Tim, be T
Michelle's and Tim's speeds are 95 k/h and 75 k/h, respectively
So, distance covered by Michelle when she gets to the catch-up point is 95T
Tim left A 48 minutes, or {{{48/60}}}hr, or {{{4/5}}}hr before Michelle
Therefore, distance covered by Tim when he gets to the catch-up point is {{{75(T + 4/5)}}} = 75T + 60
Since they covered the same distance when they met, we equate their distances to get: 95T = 75T + 60
                                         95T - 75T = 60
                                               20T = 60
Time Michelle took to catch up to Tim, or {{{highlight_green(matrix(1,5, T, "=", 60/2, "=", highlight(matrix(1,2, 3, hours))))}}}

In 3 hours, Michelle caught up with Tim. In addition, Michelle completed the 285-km trip in {{{285/95}}} = 3 hours. So,
Michelle caught up with Tim at the end-point (B). So, both reached B, the end point, at the same time, with Michelle
taking 3 hours, and Tim: {{{3 + 4/5 = 3&4/5}}} hours, thereby making Tim 0 km from B when Michelle completed the 285-km trek, from A to B.</pre>