Question

Macie and Seth built sandcastles at the beach. Macie's
sandcastle was 220 cm tall but the wind is blowing away
sand at a rate of 4.8 cm per minute. Seth's sandcastle is 132
cm tall and he is adding sand to it at a rate of 6.2 cm per
minute.

Answer 1

I guess that we want to know when both sandcastles will have the same height. We will see that the castles will have the same height after 8 minutes.

We know that Macie sandcastle height is equal to 220cm and wind blows away sand at a rate of 4.8cm per minute, then the height equation is:

M(t) = 220cm - 4.8cm*t

Where t is time in minutes.

While Seth's sandcastle has an initial height of 132cm and its height increases at a rate of 6.2 cm per minute, then the equation is:

S(t) = 132cm + 6.2cm*t

The castles will have the same height when:

M(t) = S(t)

220cm - 4.8cm*t =  132cm + 6.2cm*t

220cm - 132cm = 6.2cm*t + 4.8cm*t

88cm = 11cm*t

88cm/11cm = t = 8

This means that the castles will have the same height after 8 minutes.

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