Question

Помогите ПОЖАЛУЙСТА решить задачу. Знайка сконструировал землеройную машину, которая за 8ч может вырыть траншею, имеющая форму прямоуг. параллел., длиной 150м, глубиной 80см и шириной 60см. Сколько кубометров земли выкапывает эта машина за 1ч. Работу скольких коротышек выполняет эта машина, если за 8ч один коротышка может выкопать 240 дм². P. S. десятичные дроби не проходили

Answer 1

(150*0,8*0,6)/8=9 m^3 в час
9000/(240/8)=300 коротышек

Answer 2

To find the volume of earth excavated by the machine in 1 hour, we need to calculate the volume of the trench and divide it by 8 (since the machine completes the trench in 8 hours).

Calculating the Volume of the Trench:

The trench has the shape of a rectangular prism with a length of 150 meters, a depth of 80 centimeters, and a width of 60 centimeters. To find the volume, we multiply these dimensions together:

Volume of the trench = length x depth x width

Let's convert the depth and width to meters to maintain consistent units:

Depth = 80 centimeters = 0.8 meters Width = 60 centimeters = 0.6 meters

Now we can calculate the volume:

Volume of the trench = 150 meters x 0.8 meters x 0.6 meters

To find the volume in cubic meters, we multiply the above values:

Volume of the trench = 72 cubic meters

Calculating the Volume Excavated in 1 Hour:

Since the machine completes the trench in 8 hours, we divide the volume of the trench by 8 to find the volume excavated in 1 hour:

Volume excavated in 1 hour = Volume of the trench / 8

Substituting the value of the volume of the trench:

Volume excavated in 1 hour = 72 cubic meters / 8

Volume excavated in 1 hour = 9 cubic meters

Therefore, the machine excavates 9 cubic meters of earth in 1 hour.

Calculating the Number of Gnomes' Work:

If one gnome can excavate 240 square decimeters (dm²) in 8 hours, we can calculate the area excavated by one gnome in 1 hour:

Area excavated by one gnome in 1 hour = 240 dm² / 8

Area excavated by one gnome in 1 hour = 30 dm²

Since the trench has a width of 60 centimeters (0.6 meters), we can calculate the length of the trench excavated by one gnome in 1 hour:

Length excavated by one gnome in 1 hour = Area excavated by one gnome in 1 hour / Width

Length excavated by one gnome in 1 hour = 30 dm² / 0.6 meters

Length excavated by one gnome in 1 hour = 50 meters

To find the number of gnomes required to excavate the entire trench in 8 hours, we divide the length of the trench (150 meters) by the length excavated by one gnome in 1 hour (50 meters):

Number of gnomes = Length of the trench / Length excavated by one gnome in 1 hour

Number of gnomes = 150 meters / 50 meters

Number of gnomes = 3

Therefore, the machine can complete the work of 3 gnomes in 8 hours.

I hope this helps! Let me know if you have any further questions.