Problem

The capacity of a dump truck is listed by the manufacturer as $10 \mathrm{yd}^{3}$. A construction site requires the removal of $170 \mathrm{~m}^{3}$ of dirt, and the contractor has three identical trucks. How many trips will each need to make? Each truck will need to make trips.

Solution

Step 1 :First, we need to convert the volume of dirt from cubic meters to cubic yards because the capacity of the dump truck is given in cubic yards. We use the conversion factor of 1.30795, so the volume of dirt in cubic yards is \(170 \times 1.30795 = 222.3515 \mathrm{yd}^{3}\).

Step 2 :Next, we calculate the total capacity of the three trucks, which is \(3 \times 10 = 30 \mathrm{yd}^{3}\).

Step 3 :Then, we divide the total volume of dirt by the total capacity of the three trucks to find out how many trips are needed. This is \(\frac{222.3515}{30} = 7.4117\) trips.

Step 4 :Since a truck cannot make a fraction of a trip, we will need to round up to the nearest whole number. Therefore, each truck will need to make \(\boxed{8}\) trips.

From Solvely APP
Source: https://solvelyapp.com/problems/31443/

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