Question

Two hourglasses are turned over at the exact same time. The first hourglass contains 300 grams of sand in the upper bulb and sand flows down into the lower bulb at a rate of 5 grams per minute. The second hourglass contains 200 grams of sand in the upper bulb and sand flows down into the lower bulb at a rate of 2 grams per minute. determine the approximate number of minutes it takes for the amount of sand in the top bulbs of the hourglasses to be equal.

Answer 1

Answer:

33⅓ minutes, or 33 minutes 20 seconds

Step-by-step explanation:

Let's say t is time in minutes.

The amount of sand in the top of the first hourglass is 300 − 5t.

The amount of sand in the top of the second hourglass is 200 − 2t.

When they are equal:

300 − 5t = 200 − 2t

100 = 3t

t = 33⅓

It takes 33 minutes and 20 seconds for the amount of san in the top bulbs of the hourglasses to be equal.

Answer 2

The amount of sand is an illustration of linear equations

The amount of sand in the hourglasses would be equal after 33.33 minutes

Let time be represented by t

For the first hourglass, we have:

• Initial = 300 grams
• Rate = -5 grams per minute (because it reduces)

So, the function for the first hourglass is:

$\mathbf{f(t) = 300 -5t}$

For the second hourglass, we have:

• Initial = 200 grams
• Rate = -2 grams per minute (because it reduces)

So, the function for the second hourglass is:

$\mathbf{g(t) = 200 -2t}$

When the amount of sand in each hourglass are equal, we have:

$\mathbf{f(t) = g(t)}$

So, we have:

$\mathbf{300 - 5t = 200 - 2t}$

Collect like terms

$\mathbf{5t - 2t =300 - 200}$

$\mathbf{3t =100}$

Divide both sides by 3

$\mathbf{t =\frac{100}3}$

$\mathbf{t =33.33}$

Hence, the amount of sand would be equal after 33.33 minutes

Read more about linear equations at:

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