Question

Trucks begin removing gravel from two different piles at the same time. Pile A holds 255 tons of gravel initially, and the gravel is removed at a rate of 20 tons per hour. Pile B holds 220 tons of gravel initially, and the gravel is removed at a rate of 15 tons per hour. After a certain number of hours, the amount of gravel remaining in Pile A equals the amount of gravel remaining in Pile B. At that time, how many tons of gravel will remain in each pile? 70 tons 105 tons 115 tons 140 tons

Answer 1

115 tons for both piles.

Explanation:

Let's use "h" to represent the number of hours it takes for both piles to have the same amount of gravel remaining.

The amount of gravel remaining in Pile A after "h" hours can be represented as:

255 - 20h

Similarly, the amount of gravel remaining in Pile B after "h" hours can be represented as:

220 - 15h

We know that at this point, the amount of gravel remaining in Pile A will equal the amount of gravel remaining in Pile B, so we can set the two expressions equal to each other and solve for "h":

255 - 20h = 220 - 15h

35 = 5h

h = 7

After 7 hours, Pile A will have:

255 - 20(7) = 115 tons of gravel remaining

After 7 hours, Pile B will have:

220 - 15(7) = 115 tons of gravel remaining

Therefore, the answer is 115 tons for both piles.

Answer 2

Answer: after 7 hours, there will be 115 tons of gravel remaining in both Pile A and Pile B.

Explanation:

Let t be the number of hours since both trucks began removing gravel. The amount of gravel remaining in Pile A after t hours can be represented by the function:

A(t) = 255 - 20t

Similarly, the amount of gravel remaining in Pile B after t hours can be represented by the function:

B(t) = 220 - 15t

To find the time at which the amount of gravel remaining in both piles is equal, we can set the two functions equal to each other and solve for t:

255 - 20t = 220 - 15t

35 = 5t

t = 7

After 7 hours, the amount of gravel remaining in both piles will be equal. To find the amount of gravel remaining in each pile at that time, we can plug in t = 7 into the two functions:

A(7) = 255 - 20(7) = 115

B(7) = 220 - 15(7) = 115