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iacamp
Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 5.0 mi/h, the time to go one mile decreases by 12 s. What was your original speed?
The original speed is 1/t mi/h. The increased speed is 1/t + 5 mi/h. The time to go one mile at the increased speed is given by: \[\large \frac{1}{\frac{1}{t}+5}\ .......(1)\] We can equate the time in (1) with the decreased time to go one mile as follows: \[\large \frac{1}{\frac{1}{t}+5}=t-\frac{12}{3600}\ .........(2)\] Manipulation of (2) produces the following quadratic equation: \[\large 1500t ^{2}-5t-1=0\ ...........(3)\] The real solution of (3) gives the original time to travel one mile as a decimal fraction of an hour. The reciprocal gives the original speed in mi/h.