Very, Very Hard

Question

A hiking group are on a five-day trip. On the first day they covered 1/4 of the total distance. The next day they cover 1/4 of the remaining distance. On the 3rd day they cover 2/5 of the remainder, and on the 4th day they cover 1/2 of the distance left. They now have 14 miles left, how much have they walked?

Answer 1

Let d = the total distance the group walks.

 

First work on the fractions:

 

After Day 1:  3/4 of the distance remains

On day 2, they cover 1/4 of the remaining 3/4, which is 3/16, so they have 3/4 - 3/16 left or 9/16

On day 3, they cover 2/5 of the remaining 9/16, which is 9/40, so they have 9/16 - 9/40 left or 27/80

On day 4, they cover 1/2 of the remaining 27/80, which is 27/160, so they have 27/80 - 27/160 left or 27/160.

 

Whew!  That fraction remaining is equal to the 14 miles remaining, so

 

27d/160 = 14

 

You can do the algebra here, I think, but it comes out to 2240/27 or just less than 83 miles (82.96).

 

Since the fractions used in the problem itself are easily convertible to decimals, you could do the problem that way, as well.