Units of measurement in average speed

 Units of measurement in average speed

Example: 1
If a car is traveling at an average speed of 45 miles per hour, how many miles does the car travel in 20 minutes?
Average speed of 45 miles per hour means that at an average the car is traveling 45 miles in 1 hour. The two units of measurement are miles and hour. 
Since 20 minutes is one-third of 1 hour (60 minutes), the distance traveled will also be one-third. One-third of 45 miles is 15 miles.
Be consistent with the time. It is best to convert hour to minutes in solving such questions.

Explanation:
The ratio of the two units of measurement will always be same for a given speed. The ratio of miles:hour in the above example is 45 miles:1 hour. For any value of miles or hour, this ratio will be same. 
Since 1 hour is 60 minutes, the ratio of miles:minutes will always be 45 miles:60 minutes.
Hence,
miles:minutes  =  45 miles:60 minutes  =  unknown miles:20 minutes
Since 20 is one-third of 60, unknown miles will be one-third of 45.
The above example is a simple question that can be solved using mental math. See Example 2 below, where numbers are not so obvious. 

Example: 2
If a train is traveling at an average speed of 125 miles per hour, how many miles does the train travel in 85 minutes, rounded to the nearest tenth?
Convert hour to minutes and set up a proportion for miles and minutes. Let the miles in 85 minutes be 𝒙.
$$\boldsymbol{\frac {miles}{minutes}=\frac {125}{60}=\frac {x}{85}}$$
Cross multiply and solve for 𝒙.
60 × 𝒙  =  125 × 85
60𝒙  =  10,625
𝒙  =  177.083 miles
Round to nearest tenth  =  177.1 miles

Explanation on proportion:
Proportion is a ratio written as a fraction. Hence, similar ratios can be equated as fractions. Since the train is traveling at an average speed of 125 miles in 60 minutes (1 hour), the ratio of miles:minutes is 125:60  =  unknown mile:85. This can be written as fractions as shown in the solution above.

Try the following:
1.  Josie is riding a bicycle at an average speed of 12 miles per hour. How many miles will Josie ride in 15 minutes?
2.  A taxi is traveling at an average speed of 35 miles per hour. How many miles will the taxi travel in 85 minutes?
3.  If a bus is traveling at an average speed of 25 miles per hour, how many minutes will it take for the bus to travel 70 miles?

Show/Hide Answers
1.  Since 15 minutes is one-fourth of 1 hour (60 minutes), the distance traveled will also be one-fourth. One-fourth of 12 miles is 3 miles.
2.  
$${\frac {miles}{minutes}=\frac {35}{60}=\frac {x}{85}    →    {x=49.58}\ {miles}}$$
3.  
$${\frac {miles}{minutes}=\frac {25}{60}=\frac {70}{x}    →    {x=168}\ {minutes}}$$