The car and the train are traveling at the same speed.
Practice makes perfect
A ratio is a comparison of two quantities. If we consider two quantities a and b, the ratio a:b indicates that there are a units of the first quantity for every b units of the second quantity.
a/b or a:b
Ratios occur in everyday life in countless scenarios. Let's see a few examples!
Scenario
Ratio Notation
Gasoline consumption when traveling by car
Miles per gallon = Miles traveled/Gallons of gasoline
Types of fruit in a bowl
Apples : Bananas
Rate of travel, according to the distance formula
Rate = Distance/Time
Demographics of a school classroom
Students who take the bus:Students who walk
We are given that a train moving at a constant speed travels 3 miles every 5 minutes and that a car moving at a constant speed travels 12 miles every 20 minutes. We want to know if the vehicles are traveling at the same speed. Let's start by rewriting each speed as a ratio.
3 miles every 5 minutes → 3:5
12 miles every 20 minutes → 12:20
Now we need to determine whether the ratios are equivalent. Recall that two ratios are equivalent when we can multiply each quantity in one ratio by the same positive number to obtain the other ratio. Let's see an example!
We can use this information to see if the given ratios are equivalent.
We can get the train ratio by multiplying the car ratio by 4. Therefore, the vehicles are traveling at the same rate of speed.
