Problem solving-Hiking

Question

Gary can hike on level ground 3 mile an hour faster than he can on uphill terrain. Yesterday, he hiked 34 miles, spending 2 hours on level ground and 5 hours on uphill terrain. What is his average speed on level ground?

Answer 1

Kailynn:

 

The crucial relation to remember in such problems is....distance traveled = speed multiplied by time taken to travel.

 

Let Gary's average speed on level ground be x mph. (Usually, it is good to take as x, what is asked).   Then from the info

 

given, his rate uphill is (x - 3).  We are given that he spent 2 hours on level ground. So he traveled x (2) = 2x  miles on level ground. He traveled 5 hours uphill, so he traveled 5(x-3) miles uphill.  The total distance he hiked was 2x + 5(x-3) miles. We are also given that the total distance of his hike was 34 miles.  Equate the two quantities for total distance.

 

2x + 5(x-3) = 34

 

7x = 34 + 15 = 49

 

x = 49/7 = 7.

 

Always write your answer in context.  Gary's average speed on ground was 7 mph.  Done.

 

Dr. G.

 

P.S. Always back check too.  Here it is easy.