Question

Hannah's sandcastle is 180cm tall,but the wind is blowing away sand at a rate of 3cm per minute. Devin's sandcastle is 160cm tall and he is adding sand to it at a rate of 2cm per minute. After how many minutes will their sandcastles be the same height?

Answer 1

Hanna

Sandcastle's height: 180 cm

sand blew away = 3 cm per minute (negative)

Devin

Sandcastle's height = 160m

San added = 2 cm per minute

We have to write an equation for each one:

Hanna

y=180-3x

Where y is the height of the castle and x is the number of minutes

Devin:

y= 160+2x

Since both heights must be equal:

y=y

180-3x=160+2x

Solve for x (minutes)

180-160 = 2x+3x

20 = 5x

20/5 = x

4=x

After 4 minutes