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