Jeremy and Cynthia leave at the same time to travel 75 miles to an area. Jeremy drives 15 miles in 12 minutes. Cynthia drives 26 minutes in 20 minutes. If they continue at the same rates, who will arrive at the area first?
Cynthia. Find the unit rate of each. 15 / 12 = 1.25 miles per minute. 26 / 20 = 1.3 miles per minute. The 1.3 is faster which means will arrive first.
To determine who will arrive at the area first, we need to compare their rates of travel. The rate of travel is calculated by dividing the distance traveled by the time taken.
Let's start with Jeremy's rate of travel:
Jeremy drives 15 miles in 12 minutes.
Rate of travel = Distance / Time
Rate of travel = 15 miles / 12 minutes
To compare their rates fairly, let's convert Cynthia's time to the same unit:
Cynthia drives 26 miles in 20 minutes.
Now, let's calculate Cynthia's rate of travel:
Rate of travel = Distance / Time
Rate of travel = 26 miles / 20 minutes
To compare their rates, we need to calculate the rate per minute.
Jeremy's rate of travel = (15 miles / 12 minutes) = 1.25 miles/minute
Cynthia's rate of travel = (26 miles / 20 minutes) = 1.3 miles/minute
Comparing the rates, Cynthia's rate of travel is slightly higher than Jeremy's.
Therefore, Cynthia will arrive at the area first since she is traveling at a slightly faster rate.