Question

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?

Answer 1

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.