Since you hike [tex] \frac{2}{3}[/tex] miles every [tex]\frac{1}{4}[/tex] hour, you'll hike [tex]\frac{2}{3}*4=\frac{8}{3}=2\frac{2}{3}[/tex] every hour. Comparing this to your friend's rate, we can see that you hike more miles in one hour. You hike [tex]\frac{\frac{8}{3}}{\frac{7}{3}}=\frac{8}{3}*\frac{3}{7}=\frac{8}{7}[/tex] times faster.
a) You hike faster. You hike [tex]\frac{8}{7}[/tex] times faster.
The two of you will meet when the total distance you've traveled sum up to [tex]17.5[/tex] miles. You can find the distance both you and your friends traveled by multiplying your rate with the time you've been hiking. Since you both need to arrive at the same time, we will assign the same variable, t, to determine after how many hours you will meet.
[tex] \frac{8}{3}t+ \frac{7}{3}t=17.5 [/tex]
[tex] \frac{15}{3}t=17.5 [/tex]
[tex] t=17.5*\frac{3}{15}=3.5 [/tex]
b. The two of you will meet after 3.5 hours.
As said earlier, we just multiply the rate with the number of hours you've traveled to find the distance you've hiked.
You traveled: [tex] \frac{8}{3}* \frac{7}{2} = \frac{28}{3}=9.33 [/tex] miles
Your friend traveled: [tex] \frac{7}{3}* \frac{7}{2} = \frac{49}{6}=8.17 [/tex] miles
You hiked [tex] \frac{28}{3}-\frac{49}{6} = \frac{7}{6}=1.167 [/tex] miles farther.
c)You hiked farther. You hiked 1.167 miles farther.
