How many miles have they walked?

Question

A group on a sponsored hike covered one eighth of the total distance on the first day.

The next day they covered one quarter of what was left.

The following day they covered two fifths of the remainder and on the fourth day half of the remaining distance.

The group now have 12 miles left.

How many miles have they walked?

Answer 1

Let X = total distance
On the first day, they walked X/8 being remaining distance 7X/8
On the second day, they walked 1/4 x 7X/8 = 7/32 X remaining distance X - ( 1/8 X + 7/32 X ) = 21/32 X
On the third day they walked 2/5 x 21/32 X = 21/80 X remaining distance X - (1/8 X + 7/32 X + 21/80 X ) = 126/320 X
On the fourth day they walked 1/2 x 126/320 X = 63/320 X remaining distance X -( 1/8X+7/32X+21/80X+63/320X) = 12
Solving the equation:
X - ( 1/8 X + 7/32 X + 21/80 X + 63 /320 X ) = 12 gives X = 60,95
Therefore the total doistance walked equals to 60,95 - 12 = 48,95 miles