+0

# Take A Hike

+5
710
3
+82944

A man goes out hiking.......on the first part of the trip over level ground, his rate is 4 miles per hour.......then he hikes uphill at 3 mph.

On the return trip......the "uphill" part is now the "downhill"  part and he is able to hike at 6 miles per hour.  Then, finishing up on the level part, he once again is able to maintain the 4 miles per hour pace, as before.

The question is.........how far did he hike if the entire trip took 5 hours......?????

CPhill  Dec 12, 2015

### Best Answer

#1
+5

Let x = miles on flat land, y = miles on the hill.  He goes out and back, so total miles = 2 (x+y).

The times spent on each segment is the distance travelled divided by the speed:

x/4mph + y/3mph + x/4mph + y/6mph = 5 hours

Multiply both sides by 12 mph to clear the denominator of the fractions; the numbers are now all in miles:

3x + 4y + 3x + 2y = 6x + 6y = 6(x+y) = 12*5 = 60.

So (x+y) = 60/6 = 10 miles ... so the total distance is 20 miles.

Guest Dec 12, 2015
Sort:

### 3+0 Answers

#1
+5
Best Answer

Let x = miles on flat land, y = miles on the hill.  He goes out and back, so total miles = 2 (x+y).

The times spent on each segment is the distance travelled divided by the speed:

x/4mph + y/3mph + x/4mph + y/6mph = 5 hours

Multiply both sides by 12 mph to clear the denominator of the fractions; the numbers are now all in miles:

3x + 4y + 3x + 2y = 6x + 6y = 6(x+y) = 12*5 = 60.

So (x+y) = 60/6 = 10 miles ... so the total distance is 20 miles.

Guest Dec 12, 2015
#2
+82944
0

Very nice, Guest......I know two other ways of solving this [ there may be more].......but......I like the way you did it, maybe best of alll.....!!!!

I'll post my method in a while......it's a little different

CPhill  Dec 12, 2015
edited by CPhill  Dec 12, 2015
#3
+5

Since he hikes on the level part of his trip at an average of 4mph, therefore it takes:

1/4 hour to hike 1 mile. And,

Since he hikes on the steep part of his trip at an average of 3mph, therefore it take:

1/3 hour to hike 1 mile. Then we have:

1/4+1/3=7/12 hours-combined average of the the two rates.

Since the total hike took 5 hours or 300 mintutes, therefore we have:

7/12 X 300=175 minutes-total time for the outgoing hike.But we have:

3/(3+4) X 175=75 minutes that would take him to hike the level part of trail. And, since he hikes on this part of trail at 4mph, therefore he must hike:

75/60 X 4=5 miles-the level part of the hike. Similar calculation will give:

100/60 X 3=5 miles-the steep part of his trail. So, naturally the total outging distance is:

5+5=10 miles X 2=20 miles the total hike distance back and forth. To summarize then:

On the outgoing hike he walks for:

1.25 hours at 4mph, and 1 2/3 hours at 3mph=10 miles in 2 hours and 55 minutes.

On the returning hike he walks for:

50 minutes or 5/6 hours at 6mph and 1.25 hours at 4mph=10 miles in 2 hours and 5 minutes.

This accounts for every part of his hike and the time and distance it took him to walk the whole trail.

Guest Dec 13, 2015

### 21 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details