logic
posted by Dell on .
A son and his father take a daily walk up a hill. It is 1.5 km to the top of the hill. As the father gets older he can only walk half the speed of his son. So they start together but the father trails his son. The father reaches the halfway point when the son is at the top. The father continues to walk up as the son begins to walk down. When they meet the father turns around and walks back down the hill with his son. How far does the father walk?

Make a sketch on a number line
On the way up, the father has walked (1/2)of 1.5 km = .75 km
Let the distance walked by the father from the halfway point to when he meets his son coming back be x km, so the son would have walked 2x on his downward trip when they meet.
x + 2x = .75
x = .25
So the father then also turns around
Total walked by the father
= 4x + x + x + 4x
= 10x = 10(.25)
= 2.5 km 
thanks

Where does the 4x come from? x+2x is half the distance, so 3x is half the distance.
So, the father walked half the distance + x uphill, then the same distance downhill.
Would it not be
3x + x + x + 3x = 8x = 2.0 km?
Say the son walks at .5 km/hr and the father at .25 km/hr
So, in 3 hours the father has walked .75km (halfway) while the son has walked all the way (1.5 km)
In the next hour, the father has walked an additional .25km uphill, while the son has walked .5km downhill and they meet. By now the father has walked 1 km. He walks the same 1km downhill, making 2km. 
The total distance is 1.15 km
We know the father is only making it half the distance of the son so when the son gets to the top the father is halfway up
1.15/2=.75 km walked
The father continues up half the remaining distance to meet the son
.75/2=.375 km walked
The father and son continue that whole distance down
.75+.375=1.125 km walked
.75km +.375km + 1.125km= 2.25 km walked
The father walked 2.25 km 
1.15 km?