A car traveling at a constant rate covers miles in minutes. At this rate, how many miles will the car travel in hours?
For constant-rate word problems, first make all time units consistent (convert hours to minutes or minutes to hours), then either compute the unit rate (such as miles per minute) or use a proportion. Scale the distance by the same factor that you scale the time, keeping track of units at each step to avoid common conversion mistakes.
Hints
Make the time units match
The rate is given in miles per 15 minutes, but the question asks about 2 hours. How many minutes are in 2 hours?
Compare the two times
Once you know how many minutes are in 2 hours, compare that number to 15 minutes. By what factor does the time increase from 15 minutes to the total number of minutes in 2 hours?
Use the constant rate
If the time is multiplied by that factor, what should you do to the 18 miles to find the distance for the longer time, assuming the speed is constant?
Desmos Guide
Use Desmos to scale the distance
In a new expression line, type 18/15*120 to represent 18 miles per 15 minutes times 120 minutes. The value that Desmos outputs is the number of miles the car will travel in 2 hours.
Step-by-step Explanation
Match the time units
The problem gives the rate in minutes but asks about hours. Convert 2 hours to minutes so the time units match:
- hours minutes.
Now compare 15 minutes and 120 minutes.
Find how many times longer 120 minutes is than 15 minutes
The car travels 18 miles in 15 minutes. To scale up from 15 minutes to 120 minutes, find the factor:
- .
So 120 minutes is 8 times as long as 15 minutes.
Scale the distance by the same factor
Because the car travels at a constant rate, if the time is multiplied by 8, the distance is also multiplied by 8:
- Distance in 120 minutes miles.
- miles.
So the car will travel 144 miles in 2 hours, which corresponds to answer choice D.