How do you write each real-world example as a rate using labels and then the unit rate: Mrs. Thomas charges $60 for 120 minutes of tutoring?

1 Answer
Feb 27, 2017

Answer:

See the explanation

Explanation:

Let time be #t#
Let cost be #c#

Basing unity to be time

The units of measurement for time in the question is given as minutes. #color(brown)("So using the same unites as in the question we have:")#

Using ratio: #("cost")/("time") ->c/t=($60)/120#

To make unit time we need to convert the 120 minutes into 1 minute

So we have: #($60.00-:120)/(120-:120) = ($0.50)/1#

For unit time to be 1 minute the charge is $0.50
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(brown)("However, unit charge is normally stated as cost per hour. ")#

So to change this to that form we need 60 minute

#($0.50xx60)/(1xx60) = ($30)/(60" minute")#

But 60 minutes is the same as 1 hour giving:

#($30)/(1" hour")#