four people want to cross the river. there is only one boat available and it can carry and maximum of 200 pounds. the weights of four people are 190, 180, 120, and 80 pounds. each tune the boat crosses the river from on shore to the other is counted as one crossing of the boat. what is the minimum number of crossings required for the boat
The minimum number of crossings required for the boat to get all four people across the river can be achieved as follows:
1. First, the two lightest people, weighing a total of 80 pounds, cross together. This is the first crossing.
2. One of the two lightest people, weighing 80 pounds, goes back alone. This is the second crossing.
3. The two heaviest people, weighing a total of 370 pounds, cross together. This is the third crossing.
4. One of the two heaviest people, weighing 190 pounds, goes back alone. This is the fourth crossing.
5. The two lightest people, weighing a total of 200 pounds, cross together. This is the fifth crossing.
Therefore, the minimum number of crossings required for the boat to get all four people across the river is 5 crossings.
To minimize the number of crossings required for the boat to transport all four people across the river, we can follow these steps:
1. The heaviest person (190 pounds) crosses the river first.
- One crossing has been completed, and the remaining capacity of the boat is 200 - 190 = 10 pounds.
2. The lightest person (80 pounds) returns with the boat.
- Two crossings have been completed, and the remaining capacity of the boat is 200 - 80 = 120 pounds.
3. The next heaviest person (180 pounds) crosses the river with the lightest person (80 pounds).
- Three crossings have been completed, and the remaining capacity of the boat is 120 - 180 = -60 pounds. (Negative weight indicates that the boat is overloaded)
4. The lightest person (80 pounds) returns with the boat.
- Four crossings have been completed, and the remaining capacity of the boat is -60 + 80 = 20 pounds.
5. The heaviest person (190 pounds) crosses the river again.
- Five crossings have been completed, and the remaining capacity of the boat is 20 - 190 = -170 pounds.
6. The lightest person (80 pounds) returns with the boat.
- Six crossings have been completed, and the remaining capacity of the boat is -170 + 80 = -90 pounds.
7. The next heaviest person (180 pounds) crosses the river with the lightest person (80 pounds) again.
- Seven crossings have been completed, and the remaining capacity of the boat is -90 - 180 = -270 pounds.
8. The lightest person (80 pounds) returns with the boat.
- Eight crossings have been completed, and the remaining capacity of the boat is -270 + 80 = -190 pounds.
9. The heaviest person (190 pounds) crosses the river one more time.
- Nine crossings have been completed, and the remaining capacity of the boat is -190 - 190 = -380 pounds.
10. Finally, the last person (120 pounds) crosses the river with the heaviest person (190 pounds).
- Ten crossings have been completed, and all four people have successfully crossed the river.
Therefore, the minimum number of crossings required for the boat to transport all four people across the river is 10.