A dump truck weighs 11.2511.25 tons when empty. A conveyor belt pours sand into the truck at a constant rate of \frac{1}{4} 4
1
​
ton per minute until it is full.

Let tt represent the elapsed time in minutes. Let ww represent the weight of the truck after tt minutes.
​Write an equation for ww in terms of tt.

​Enter your equation in the box provided. Enter only your equation.

​

w=w=
1
$$

​

​Part B

The dump truck from Part A weighs 1818 tons when filled. At the same time the dump truck is being filled, an identical dump truck filled to capacity is being emptied at a rate of \frac{1}{8}
8
1
​
ton per minute.

How much sand is in each dump truck when the trucks are the same weight?

​Enter your answer in the box.

​

Step-by-step explanation:

A. For this case, the first thing we must do is define variables.

We have then:

t: time in minutes

The linear equation that represents the problem is given by:

w (t) = (1/4) t + 11.25

An equation for W in terms if T is:

w (t) = (1/4) t + 11.25

B. 2 .25 Tons

Step-by-step explanation:

Weight of truck + sand when filled= 18 tons

Discharge rate per minute= 1/8 tons/ minute

Quantity of sand in the truck will be:

1/8tons per minute×18tons = 9/4 = 2.25tons

Step-by-step explanation:

Let's say the length is l and the width is w. Since the problem says that the length is "six times the quantity of five less than half its width", we can write the equation:

l = 6 * (w/2 - 5)

Now, the area of a rectangle is of the form: A = lw, where l is the length and w is the width. We can substitute the expression of l above into the equation:

Hope this helps!