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\(T_1\): 4
\(T_2\): 5
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
35% (03:18) correct
65%
(03:20)
wrong
based on 239
sessions
History
Date
Time
Result
Not Attempted Yet
On Christmas Eve, Santa and 5 of his elves need to deliver 210 presents to 7 towns, with each one requiring exactly 30 presents. Each trip to a town and back takes 1 hour, several trips can be made simultaneously, and each one requires at least Santa or two elves. Santa can deliver at most 15 presents per trip, and each elf can deliver at most 10 presents per trip.
Based on the information above, select for \(T_1\) the number of minimum hours it will take to deliver all 210 presents with Santa and \(T_2\) the number of minimum hours it will take to deliver all 210 presents without Santa.
Based on the information above, select for \(T_1\) the number of minimum hours it will take to deliver all 210 presents with Santa and \(T_2\) the number of minimum hours it will take to deliver all 210 presents without Santa.
| \(T_1\) | \(T_2\) | |
| 2 | ||
| 3 | ||
| 4 | ||
| 5 | ||
| 6 | ||
| 7 |
ShowHide Answer
Official Answer
\(T_1\): 4
\(T_2\): 5
25 Dec 2024, 01:52
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Santa =15 gifts
5 Elves = 10*5 gifts= 50
T1 the number of minimum hours it will take to deliver all 210 presents with Santa:
Each round we have : 1 Santa and 5 Elves (Need at least 2 elves)
Gifts in each round= 15+50=65
Total gifts: 210
Minimum rounds required between 210[url=>]>[/url]65*n (65*3= 195 and 65*4= 260)
Each trip to a town and back takes 1 hour, Therefore answer is 4 hours
T2 the number of minimum hours it will take to deliver all 210 presents without Santa:
Each round we have : 5 Elves (Need at least 2 elves)
Gifts in each round= 50
Total gifts: 210
Minimum rounds required between 210[url=>]>[/url]50*n (50*4= 200 and 50*5= 250)
Each trip to a town and back takes 1 hour, Therefore answer is 5 hours
5 Elves = 10*5 gifts= 50
T1 the number of minimum hours it will take to deliver all 210 presents with Santa:
Each round we have : 1 Santa and 5 Elves (Need at least 2 elves)
Gifts in each round= 15+50=65
Total gifts: 210
Minimum rounds required between 210[url=>]>[/url]65*n (65*3= 195 and 65*4= 260)
Each trip to a town and back takes 1 hour, Therefore answer is 4 hours
T2 the number of minimum hours it will take to deliver all 210 presents without Santa:
Each round we have : 5 Elves (Need at least 2 elves)
Gifts in each round= 50
Total gifts: 210
Minimum rounds required between 210[url=>]>[/url]50*n (50*4= 200 and 50*5= 250)
Each trip to a town and back takes 1 hour, Therefore answer is 5 hours
25 Dec 2024, 07:00
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1. Let’s split the problem into 2 parts.
2. Part 1: finding \(T_1\). Santa and 5 of his elves can deliver at most \(15 + 10 * 5 = 65\) presents per hour. \(\frac{210}{65} \approx 3.23 > 3\). So, in theory, 4 hours is the least. Now, let’s build an example.
Note: +15 - Santa arrived, +10 * 3 - 3 elves delivered maximum, +10 * 2 - 2 elves delivered maximum, +10+0 - 1 elf delivered 10 while the other was with them (since at least 2 must be on a trip).
3. Part 2: finding \(T_2\). 5 of Santa’s elves can deliver at most \(10 * 5 = 50\). \(\frac{200}{50}\) = 4. So, in theory, 4 hours is the least. However, this is under the assumption that each elf can deliver 10 presents each hour. This is impossible since you will have a town with 20 presents delivered and sending at least 2 elves will waste the possibility of giving 10 more. Now, let’s build an example for 5 hours.
Note: +15 - Santa arrived, +10 * 3 - 3 elves delivered maximum, +10 * 2 - 2 elves delivered maximum, +10+0 - 1 elf delivered 10 while the other was with them (since at least 2 must be on a trip).
4. Our answer will be: \(T_1\) - 4 and \(T_2\) - 5.
2. Part 1: finding \(T_1\). Santa and 5 of his elves can deliver at most \(15 + 10 * 5 = 65\) presents per hour. \(\frac{210}{65} \approx 3.23 > 3\). So, in theory, 4 hours is the least. Now, let’s build an example.
| Hours | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 15 (+15) | 30 (+10 * 3) | 20 (+10 * 2) | 0 | 0 | 0 | 0 |
| 2 | 30 (+15) | 30 | 20 | 30 (+10 * 3) | 20 (+10 * 2) | 0 | 0 |
| 3 | 30 | 30 | 30 (+10+0) | 30 | 20 | 30 (+10 * 3) | 15 (+15) |
| 4 | 30 | 30 | 30 | 30 | 30 (+10+0) | 30 | 30 (+15) |
Note: +15 - Santa arrived, +10 * 3 - 3 elves delivered maximum, +10 * 2 - 2 elves delivered maximum, +10+0 - 1 elf delivered 10 while the other was with them (since at least 2 must be on a trip).
3. Part 2: finding \(T_2\). 5 of Santa’s elves can deliver at most \(10 * 5 = 50\). \(\frac{200}{50}\) = 4. So, in theory, 4 hours is the least. However, this is under the assumption that each elf can deliver 10 presents each hour. This is impossible since you will have a town with 20 presents delivered and sending at least 2 elves will waste the possibility of giving 10 more. Now, let’s build an example for 5 hours.
| Hours | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 30 (+10 * 3) | 20 (+10 * 2) | 0 | 0 | 0 | 0 | 0 |
| 2 | 30 | 20 | 30 (+10 * 3) | 20 (+10 * 2) | 0 | 0 | 0 |
| 3 | 30 | 20 | 30 | 20 | 30 (+10 * 3) | 20 (+10 * 2) | 0 |
| 4 | 30 | 30 (+10+0) | 30 | 20 | 30 | 20 | 30 (+10 * 3) |
| 5 | 30 | 30 | 30 | 30 (+10+0) | 30 | 30 (+10+0) | 30 |
Note: +15 - Santa arrived, +10 * 3 - 3 elves delivered maximum, +10 * 2 - 2 elves delivered maximum, +10+0 - 1 elf delivered 10 while the other was with them (since at least 2 must be on a trip).
4. Our answer will be: \(T_1\) - 4 and \(T_2\) - 5.
