Help! I am not really good with story problems!
Forest rangers measure a depth of 82" of snow on a mountain peak at 8am. Snow is expected to fall at a steady rate of 3/4" per hour throughout the day.
A) write an equation that approximates the depth of 'y' of snow on the mountain peak 'x' hours after 8am.
B) the rangers plan to start a controlled avalanche when the depth of snow on the peak reaches 85". At what time will this be?
Thank you, thank you, thank you!!!!
A. Y = 82 + .75x
B. Substitute 85 for Y and solve for x. Add that time to 8 AM.
A) To approximate the depth of snow on the mountain peak 'y' hours after 8 am, we can use the equation:
y = 82 + (3/4)x
In this equation, x represents the number of hours after 8 am and y represents the depth of snow in inches.
B) To find out at what time the depth of snow on the peak reaches 85 inches, we need to solve the equation:
85 = 82 + (3/4)x
First, let's isolate the variable term by subtracting 82 from both sides:
85 - 82 = (3/4)x
Now, simplify the left side:
3 = (3/4)x
To solve for x, we need to isolate it. We can do this by multiplying both sides by the reciprocal of (3/4), which is (4/3):
(3)(4/3) = (4/3)(3/4)x
4 = x
So, the depth of snow on the peak reaches 85 inches approximately 4 hours after 8 am. Therefore, the controlled avalanche will occur at noon (12 pm).