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 half-way 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?
INFORMATIVA SULLA PRIVACY DELLA MISURAZIONE DIGITALE
To find out how far the father walks, let's break down the steps of their walk up the hill.
1. First, let's calculate the distance from the starting point to the halfway point. Since it is 1.5 km to the top of the hill, the halfway point will be at 1.5 km / 2 = 0.75 km.
2. The son is walking at a faster speed, so he reaches the top of the hill while the father is still walking towards the halfway point. At this point, the son has walked the full distance of 1.5 km.
3. Now, let's calculate how far the father has walked from the starting point to the halfway point. Since he walks at half the speed of his son, he covers half the distance in the same time. Therefore, when the father reaches the halfway point, he has walked 0.75 km.
4. When the father reaches the halfway point, the son starts walking down from the top of the hill. Both the father and son are now moving towards each other.
5. They meet somewhere between the halfway point and the top of the hill. At this meeting point, the father has walked 0.75 km, while the son has walked the remaining distance of 1.5 km - 0.75 km = 0.75 km.
6. After they meet, the father turns around and walks back down the hill with his son. Therefore, he covers the same distance going down as he did going up. So the distance the father walks back down the hill is also 0.75 km.
7. Now, let's add up all the distances the father has walked: 0.75 km (from the starting point to the halfway point) + 0.75 km (from the meeting point to the top) + 0.75 km (walking back down the hill) = 2.25 km.
So, the father walks a total distance of 2.25 km.