A contractor has been asked to pave 15 miles of new road. Before he can set his price, he needs to know how much the cement will cost. If the road is 45 feet wide and 9 inches thick and the cost of cement is $35 per cubic yard, what will be the cost of the cement needed for the road?
45 feet = 15 yards
9 inches = 0.25 yard
1 mile = 1760 yards; 15 miles = 26,400 yards
15 * 0.25 * 26,400 * 35 = ?
Thank You Very Much
You're very welcome.
To calculate the cost of the cement needed for the road, we first need to find the volume of the cement required.
1. Convert the measurements to the same units:
- Width: 45 feet
- Thickness: 9 inches
Since the cost of cement is usually measured in cubic yards, let's convert all the measurements to yards:
- Width: 45 feet = 45/3 = 15 yards
- Thickness: 9 inches = 9/36 = 0.25 yards
2. Calculate the volume of the cement:
- Volume = Width * Length * Thickness
- Length = 15 miles = 15 * 5280 feet (since 1 mile = 5280 feet)
- Volume = 15 yards * (15 * 5280 feet) * 0.25 yards
Now, we need to convert the volume into cubic yards since the cost of the cement is given per cubic yard.
3. Convert the volume into cubic yards:
- 1 cubic yard = 27 cubic feet
- Volume = (15 * (15 * 5280) * 0.25) / 27 cubic yards
4. Calculate the cost of the cement:
- Cost = Volume * Cost per cubic yard
- Cost = [(15 * (15 * 5280) * 0.25) / 27] * $35
Calculating this equation will give you the cost of the cement needed for the road.