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Michelle was driving to and from work one day. The time it took to drive home was ten minutes less than twice the time it took to drive to work.

(a) If t represents the amount of minutes it took Michelle to drive to work, then write and expression in terms of t for the amount of minutes it took Michelle to drive home from work.
(b) If the average time Michelle spent in her car on the way to and from work was 43 minutes, determine the amount of time, in minutes, it took her to get to work.
 
 
 
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1 Answer

We have 2 unknowns:  t = mins to drive to work
                                  h = mins to drive home from work
a) The drive home is 10 mins less than twice the drive to work:
                                  h = 2t - 10
b) The average time spent going to and returning from work is 43mins. We need to solve for t. Therefore:
                                 (t + h)/2 = 43  equation for solving the mean or average time
                                 (t + 2t -10)/2 = 43  replace h with 2t - 10 from part "a" above
                                 (3t - 10)/2 = 43  combine like terms
                                 3t - 10 = 2 X 43  multiply both sides by 2
                                 3t = 86 + 10  add 10 to both sides
                                 3t = 96
                                 t = 96/3  divide both sides by 3
                                 t = 32
Therefore, the time to get to work is:  t = 32mins