# calculate speed and time

Due to a fuel shortage, the speed limit on a major highway was lowered 5 miles per hour. Assume that a certain motorist always drives at the legal speed limit. If he were able to drive 99 miles in 2 1/5 hours at the original speed limit, how long will it take him to drive 100 miles at the new speed limit?

NOTE: the correct answer is 2 hours and 30 minutes.

• Please read the tag description before using a tag for the first time. This has nothing to do with the tag elementary-number-theory. – joriki Aug 11 '15 at 12:40

Sometimes it's just easier to use multiple variables to describe the given relationships. For example: $$V_{\text{old}} = \frac{D_\text{old}}{T_\text{old}}=\frac{99}{2\frac{1}{5}}$$ $$V_\text{new}=V_\text{old}-5$$ $$V_{new}=\frac{D_\text{new}}{T_\text{new}}=\frac{100}{T_\text{new}}\implies T_\text{new}=\frac{100}{V_\text{new}}$$ Now that you have everything in front of you, just substitute away until there is just $T_\text{new}$ remaining.
His original speed was $\frac{99 miles}{2.2 hours}=45$ mph, so the new speed limit must be $45-5=40$ mph. Thus $\frac{100 miles}{x hours}=40$ mph. Solving for x, $100/40=2.5$ hours, or 2 hours and 30 minutes.