A rectangular field has a length of 1.5 \times 10^4 meters and a width of 4.0 \times 10^3 … — ACT

A rectangular field has a length of $1.5 \times 10^4$ meters and a width of $4.0 \times 10^3$ meters. If a tractor can mow $6.0 \times 10^5$ square meters per hour, how many hours will it take the tractor to mow the entire field?

Answer: 100 hours

Answer

It will take 100 hours for the tractor to mow the entire field.

The total area of the field is the product of its length and width:

(1.5 \times 10^4) \times (4.0 \times 10^3) = 6.0 \times 10^7

square meters. Dividing this area by the tractor's mowing rate of

6.0 \times 10^5

square meters per hour gives

\frac{6.0 \times 10^7}{6.0 \times 10^5} = 1.0 \times 10^2 = 100

hours.

Step-by-Step Solution

Calculate the area of the rectangular field.

Area =

6.0 \times 10^7

square meters

The area of a rectangle is found by multiplying its length by its width:

(1.5 \times 10^4 \text{ m}) \times (4.0 \times 10^3 \text{ m}) = 6.0 \times 10^7 \text{ m}^2

Calculate the time required to mow the field.

Time =

100

hours

Divide the total area by the tractor's mowing rate:

\frac{6.0 \times 10^7 \text{ m}^2}{6.0 \times 10^5 \text{ m}^2/\text{hour}} = 1.0 \times 10^2 = 100

hours.

Key Concept

Multiplication and division of numbers in scientific notation

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