Question

If your front lawn is 16.0 feet wide and 20.0 feet long, and each square foot of lawn accumulates 1250 new snowflakes every minute, how much snow, in kilograms, accumulates on your lawn per hour? Assume an average snowflake has a mass of 1.50 mg.

Answer 1

36 kg/h

Step-by-step explanation:

We start calculating the total amount of square feet of the lawn with the rectangle area equation:

Area(rectangle)= long x wide = 20 ft x 16 ft = 320
`ft^(2)`

Now, for every one of those 320
`ft^(2)` 1250 new snowflakes accumulates each minute, this means that means that in one minute we get:

# Snowflakes (min) =
`320 ft^(2) *1250(flakes)/(ft^(2)) =400,000 snowflakes`

In a minute we have 400,000 snowflakes, then we need to multiply that by the number of minutes in an hour (60 min in an hour):

# Snowflakes (hour) =
`400,000(snowflakes)/(min)*60 (min)/(h)=24,000,000 (snowflakes)/(h)`

If each snowflake has a mass of 1.50 mg (the average), then:

`mass = 24,000,000 snowflakes*1.50(mg)/(snowflakes)=36,000,000mg`

In each kilogram there are 1000000 mg so making this transformation:

36,000,000mg to kg ⇒
`(36,000,000)/(1000000)kg=36 kg`