Question

Two towns are 1050 miles apart, a group of hikers start from each town and walk the trail toward each other. They meet after a total hiking time of 200 hours. If one group travels 1 1/2 miles Per hour faster than the other group, find the rate of each groupWhat is the rate of the slower group?What is the rate of the faster group?

Answer 1

$\begin{gathered} \text{let} \\ r=\text{rate of the slower group} \\ r+1\frac{1}{2}=\text{rate of faster group} \\ (r)(200)+(r+1\frac{1}{2})(200)=1050 \\ (r)(200)+(r+\frac{3}{2})(200)=1050 \\ (200r)+(200r+300)=1050 \\ 200r+200r+300=1050 \\ 200r+200r=1050-300 \\ 400r=750 \\ \frac{\cancel{400}r}{\cancel{400}}=\frac{750}{400} \\ r=\frac{15}{8}\text{or }1\frac{7}{8}\text{ miles per hour},\text{ rate of the slower group} \\ \\ r+1\frac{1}{2}=1\frac{7}{8}+1\frac{1}{2}=3\frac{3}{8}\text{ miles per hour, rate of the faster group} \end{gathered}$