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;

$\begin{gathered} speed=\frac{dis\tan ce}{time} \\ \text{speed}=\frac{1150}{200}=\frac{23}{4}mph \end{gathered}$

Step 2

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

x=faster group

$\begin{gathered} x-1=slower\text{ group} \\ x+x-1=\frac{23}{4} \\ 2x=\frac{23}{4}+1 \\ 2x=\frac{27}{4} \\ \frac{2x}{2}=\frac{6.75}{2} \\ x=3.375mph \end{gathered}$

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