The table shows the changes in elevation of a hiker each day for 3 days. How many miles of elevation must the hiker gain on the fourth day to gain 1/4 mile of elevation over the four days?
Day | Change in elevation
1 | -1/4
2 | 1/2
3 | -1/5
4 | ?
To find out how many miles of elevation the hiker must gain on the fourth day to gain a total of 1/4 mile of elevation over the four days, we need to add up the changes in elevation for each of the four days first.
Change in elevation for Day 1: -1/4 mile
Change in elevation for Day 2: 1/2 mile
Change in elevation for Day 3: -1/5 mile
Now, calculate the total change in elevation for the first three days:
-1/4 + 1/2 - 1/5 = -5/20 + 10/20 - 4/20 = 1/20 mile
Therefore, the hiker has already gained 1/20 mile of elevation over the first three days. To gain a total of 1/4 mile of elevation over the four days, the hiker must gain an additional:
1/4 - 1/20 = 5/20 - 1/20 = 4/20 = 1/5 mile
Therefore, the hiker must gain an additional 1/5 mile of elevation on the fourth day to gain a total of 1/4 mile of elevation over the four days.