Question

You and a friend start hiking toward each other from opposite ends of a 17.5-mile hiking trail. You hike 2/3 mile every 1/4 hour. Your friend hikes 2 1/3 miles per hour.

a. Who hikes faster? How much faster?

b. After how many hours did you meet?

c. When you meet, who hiked farther? How much farther?


Please answer this ASAP! Thank you!

Answer 1

You and a friend start hiking toward each other from opposite ends of a 17.5-mile hiking trail. You hike
2
3
23
mile every
1
4
14
hour. Your friend hikes
2
1
3
213
miles per hour.

Answer 2

Answer: a. I hike faster by
`(8)/(7)` 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 =
`(2)/(3)` ÷
`(1)/(4)`

speed =
`(2)/(3)`.4 =
`(8)/(3)`

speed = 2.667 mph

My friend hikes
`2.(1)/(3)` mph:

speed =
`(7)/(3)`

speed = 2.334 mph

Comparing the speed, I hike faster than my friend by:

`((8)/(3) )/((7)/(3) )` =
`(8)/(3) . (3)/(7)` =
`(8)/(7)` times faster.

b) Suppose time in hours is t.

I hiked a distance of
`(8)/(3)`t

My friend hiked a distance of
`(7)/(3)`t

They will meet when the sum of the distances equals 17.5 miles:

`(8)/(3).t + (7)/(3).t = 17.5`

`(15)/(3)`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:
`(8)/(3)`t

distance when we met:
`(8)/(3)`.3.5 = 9.334 miles

distance for mu friend:
`(7)/(3)`t

distance when we met:
`(7)/(3)`.3.5 = 8.167 miles

When we met, I hiked 9.334 - 8.167 = 1.167 miles farther than my friend.