Equations & inequalities word problems

The Smiths and the Johnsons were competing in the final leg of the Amazing Race. In their race to the finish, the Smiths immediately took off on a $165$165 kilometer path traveling at an average speed of $v$v kilometers per hour.

The Johnsons' start was delayed by $\dfrac{1}{2}$start fraction, 1, divided by, 2, end fraction hour. Eventually, they took a $180$180 kilometer path to the finish, traveling at an average speed that was $20$20 kilometers per hour faster than the Smiths' speed.

The Johnsons arrived at the finish line first and won the race!

Write an inequality in terms of $v$v that models the situation.