Answer: a. I hike faster by [tex]\frac{8}{7}[/tex] times faster;
b. You meet after 3.5 hours;
c. I hiked 1.167 miles farther than my friend;
Step-by-step explanation: a) To determine who hiked faster, we have to find speed of each person:
I hike 2/3 mile every 1/4 hour, so:
speed = [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{4}[/tex]
speed = [tex]\frac{2}{3}[/tex].4 = [tex]\frac{8}{3}[/tex]
speed = 2.667 mph
My friend hikes [tex]2.\frac{1}{3}[/tex] mph:
speed = [tex]\frac{7}{3}[/tex]
speed = 2.334 mph
Comparing the speed, I hike faster than my friend by:
[tex]\frac{\frac{8}{3} }{\frac{7}{3} }[/tex] = [tex]\frac{8}{3} . \frac{3}{7}[/tex] = [tex]\frac{8}{7}[/tex] times faster.
b) Suppose time in hours is t.
I hiked a distance of [tex]\frac{8}{3}[/tex]t
My friend hiked a distance of [tex]\frac{7}{3}[/tex]t
They will meet when the sum of the distances equals 17.5 miles:
[tex]\frac{8}{3}.t + \frac{7}{3}.t = 17.5[/tex]
[tex]\frac{15}{3}[/tex]t = 17.5
t = 3.5 h
After 3 and a half hours, my friend and I meet.
c) To know who hiked farther, we determine the distance my friend and I hiked when we met:
distance for me: [tex]\frac{8}{3}[/tex]t
distance when we met: [tex]\frac{8}{3}[/tex].3.5 = 9.334 miles
distance for mu friend: [tex]\frac{7}{3}[/tex]t
distance when we met: [tex]\frac{7}{3}[/tex].3.5 = 8.167 miles
When we met, I hiked 9.334 - 8.167 = 1.167 miles farther than my friend.
