Question

READ THE END! PLEASE HELP! OK, will mark best straight answer with brainiest (with explanation) URGENT! Justin's sand castle is 180 cm tall but the wind is blowing away sand at a rate of 8 cm per minute. Taylor's sand castle is 160 cm tall and she is adding sand to it at a rate of 6 cm per minute. After how many minutes will their sand castles be at an equal height? [ Also, if its 17.5 please explain what happened to 180 & 160!!! ]

Answer 1

Answer:

Both castles will have the same height at 3.33 minutes

Step-by-step explanation:

This problem will be solved with linear modeling, that is, expressing both people's sand castle's height as a function of time.

Justin built a sandcastle 180 cm tall, and its height is losing at 8 cm/min by the effect of wind. Thus, the height of Justin's sandcastle is:

$H_J=180-8t$

Where t is the time expressed in minutes.

Taylor's sandcastle is initially 160 cm tall. The wind blows away sand at 8 cm/min but she adds sand at 6 cm/min, thus the real loss of sand is 8 cm/min - 6 cm/min= 2 cm/min. Thus, the height of Taylor's sandcastle is:

$H_T=160-2t$

To find when both castles have the same height, we set:

$180-8t=160-2t$

Simplifying:

6t=20

Solving:

t=20/6=3.33\ minutes

Both castles will have the same height at 3.33 minutes