Question

A fleet of trucks hauls solid waste each week from a community of 12,000 people. Each truck can haul up to 25yd3 of solid waste with an average compaction capability of 600l bm/yd³. Each truck can make up to 6 trips per week. The community generates solid waste at a rate of 3l bm/day-person. What is the minimum number of trucks needed to service this community.

Answer 1

The minimum number of trucks needed to service the community is 1 truck.

Step-by-step explanation:

To determine the minimum number of trucks needed to service the community, we need to calculate the total volume of solid waste generated and divide it by the volume that each truck can haul.

First, we need to find the total volume of solid waste generated by the community. We can calculate this by multiplying the number of people in the community (12,000) by the rate at which each person generates solid waste (3L bm/day-person).

Total volume of solid waste generated = 12,000 people * 3L bm/day-person = 36,000 L bm/day.

Next, we need to convert the total volume of solid waste from liters to cubic yards. We can do this by dividing the total volume by the compaction capability of each truck:

Total volume of solid waste (in cubic yards) = 36,000 L bm/day / (600 L bm/yd³ * 0.350) = 17.14 yd³/day.

Finally, we divide the total volume of solid waste by the volume that each truck can haul to find the minimum number of trucks needed:

Minimum number of trucks needed = 17.14 yd³/day / 25 yd³/truck = 0.6856 trucks.

Since we can't have a fraction of a truck, we need to round up to the nearest whole number. Therefore, the minimum number of trucks needed to service the community is 1 truck.