You are pulling a raft up a river. You can make 15 miles each day. Each night, while you are asleep, however, the current pushes the raft 3 miles back downstream. If you set out on Tuesday to get to a town 85 miles upstream, on which day will you arrive?
Answer choices
1. Monday
2. Wednesday
3. Tuesday
each day you make 12 miles
After 6 days you have gone 72 miles
on the 7th day you'd make it to mile 87, so you're done.
so, what day is that?
To find out the day when you will arrive at the town, we need to calculate the number of days it will take to cover the distance of 85 miles, taking into account the daily progress and the nightly setback caused by the current.
Let's break down the problem step by step:
1. On Tuesday, you start your journey.
2. Each day, you make 15 miles of progress upstream. Therefore, after the first day (Tuesday), you will have covered 15 miles.
3. However, each night, the current pushes the raft 3 miles back downstream. So after the first night, you will be 3 miles behind your starting point because the previous day's progress was pushed back.
4. On the second day (Wednesday), you make an additional 15 miles of progress upstream. This means you will have covered a total of 15 + 15 = 30 miles by Wednesday evening.
5. But again, the current pushes the raft 3 miles back downstream during the second night. So after the second night, you will be 6 miles behind your starting point (3 miles from the first night + 3 miles from the second night).
6. On the third day (Thursday), you make another 15-mile progress upstream, bringing your total distance covered to 45 miles (30 miles from the previous day + 15 miles from the current day).
7. The current pushes the raft back 3 miles during the third night. So after the third night, you will be 9 miles behind your starting point (6 miles from the previous nights + 3 miles from the current night).
8. On the fourth day (Friday), you make another 15-mile progress upstream, bringing your total distance covered to 60 miles (45 miles from the previous day + 15 miles from the current day).
9. The current pushes the raft back 3 miles during the fourth night. So after the fourth night, you will be 12 miles behind your starting point (9 miles from the previous nights + 3 miles from the current night).
10. On the fifth day (Saturday), you make another 15-mile progress upstream, bringing your total distance covered to 75 miles (60 miles from the previous day + 15 miles from the current day).
11. The current pushes the raft back 3 miles during the fifth night. So after the fifth night, you will be 15 miles behind your starting point (12 miles from the previous nights + 3 miles from the current night).
12. On the sixth day (Sunday), you make another 15-mile progress upstream, bringing your total distance covered to 90 miles (75 miles from the previous day + 15 miles from the current day).
13. The current pushes the raft back 3 miles during the sixth night. So after the sixth night, you will be 18 miles behind your starting point (15 miles from the previous nights + 3 miles from the current night). However, you would have already arrived at the town after covering 85 miles.
Therefore, you will arrive at the town on Sunday (the sixth day), which is not given as one of the answer choices.