Why doesn’t an X percent increase in speed equal and X percent decrease in travel time?

If I am traveling 60 miles per hour and I increase my speed 10% to 66 miles per hour, why has my travel time only been reduced 9.09% and not 10%?

Thanks

Solution 1:

Your travel time is the total distance divided by your speed. If you triple your speed, you're dividing your travel time by 3. That's a 200% increase in speed and a 67% decrease in travel time. Do you still expect these percentages to be equal?

In fact, if you increase your speed by $x$%, you're multiplying it by $1+\frac x{100}$, so you're multiplying your travel time by $\frac1{1+\frac x{100}}$. If you set this fraction equal to $1-\frac y{100}$ and solve for $y$, you get $y=\frac {100x}{100+x}$. So a 10% increase corresponds to a $\frac{100\times10}{100+10}=9.09$ percent decrease.