Answer :
Final answer:
To find out how many days it would take for 3 trucks to transfer 5 kilos of sand, it is calculated based on the time it would take one truck and then adjusted for 3 trucks, resulting in approximately 10.67 days. To determine how many kilos of sand 12 trucks can transfer in 4 days, a proportion based on the initial information given for 8 trucks is used, which results in 7.5 kilos of sand.
Explanation:
Problem Solving with Ratios and Proportional Relationships
The problem at hand involves determining the relationship between the number of trucks and the amount of time taken to transfer a certain amount of sand as well as calculating the amount of sand multiple trucks can carry. We will use ratios and proportions to solve these problems.
Part A: Time Calculation for 3 Trucks
If 8 trucks can transfer 5 kilos of sand in 4 days, we can assume that 1 truck would take 8 times longer, since the number of trucks and time are inversely proportional. Therefore, 1 truck would take 8 * 4 days to transfer 5 kilos of sand. Now, to find out how many days it would take for 3 trucks, we divide the time taken by 1 truck by 3:
Time for 1 truck = 8 trucks * 4 days = 32 days
Time for 3 trucks = Time for 1 truck / 3 trucks = 32 days / 3 trucks = 10.67 days (approximately)
Part B: Sand Transfer Calculation for 12 Trucks
Given that 8 trucks transfer 5 kilos of sand, the ratio of trucks to the kilos of sand is constant. Therefore, we can set up a proportion to find out how many kilos of sand can 12 trucks transfer. Since we are keeping the number of days constant and just changing the number of trucks:
- Sand transferred by 8 trucks: 5 kilos
- Sand transferred by 12 trucks: x kilos
- Proportion: (8 trucks / 5 kilos) = (12 trucks / x kilos)
- x = (12 trucks * 5 kilos) / 8 trucks = 7.5 kilos
Therefore, 12 trucks can transfer 7.5 kilos of sand in the same 4 days.
