Question

< Two towns are 1150 miles apart. A group of hikers starts from each town and walks down the trail toward each other. They meet after a total hiking time of 200 hours. Y one group travels a mile per hour slower than the other group, find the rate of each group.The rate of the slower group isLibrary(Simplify your answer.)

Answer 1

Step 1

The total time is 200 hours

The total distance is 1150 miles

The closing speed therefore is;

`\begin{gathered} speed=(dis\tan ce)/(time) \\ \text{speed}=(1150)/(200)=(23)/(4)mph \end{gathered}`

Step 2

One group travels a mile per hour slower than the other.

x=faster group

`\begin{gathered} x-1=slower\text{ group} \\ x+x-1=(23)/(4) \\ 2x=(23)/(4)+1 \\ 2x=(27)/(4) \\ (2x)/(2)=(6.75)/(2) \\ x=3.375mph \end{gathered}`

Step 3

Find the rate of the slower group

`x-1=3.375-1=2.375\text{mph}`

Hence the rate of the slower =2.375mph

The rate of the faster group=3.375mph