A rectangular plot measures 30 meters in length and 20 meters in width. To create a platform measuring 8 meters long, 5.5 meters wide, and 1.5 meters high from the excavated soil, which increases in volume by 10/5 during digging, how deep should the field be dug?

Explanation

Let the depth of the excavation be x meters. The volume of earth dug out is 30 × 20 × x. The volume of the platform formed is 8 × 5.5 × 1.5. Since the volume of the earth increases by a factor of 10/5 (which is 2), the volume of the dug earth equals twice the volume of the platform. So, 30 × 20 × x = 2 × (8 × 5.5 × 1.5). Solving for x gives 0.10 meters or 10 centimeters.