180 miles are traveled in 4 hours, Find the ratio of miles to travel time.

Ashley Kannan | Middle School Teacher | (Level 3) Distinguished Educator

Posted on

Like many ratio problems, you would want to express this relationship as a unit rate.  This means you want to display the findings as the amount of something per another quantity.  In this instance, you want to find out a miles per hour unit rate.  You could approach this as setting up equivalent fractions, where the numerator represents miles travelled and the denominator represents hours.  In the first fraction, it would be represented as 180/4 (180 miles and 4 hours) and this would be set to X/1, because we want to find the unit rate (1 hour) and we need to know how many miles are travelled.  At this point, we could cross multiply and divide (180 * 1, then divided by 4).  The answer would be 45 miles can be travelled in one hour.  There are other ways to solve this problem, but in terms of determining unit rate, this method works well when the numbers are not so easily to manipulate as these numbers were.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

The number of miles travelled is 180 miles.The time taken for the travel is 4 hours. To find the ratio.

A ratio compares two quantities . It may be in terms of rate of one per another. We say the speed in terms of kilometer per hour. The cost per item purchased. The  'rate per unit' is actually a ratio of comparing over one unit.

But then there is a practice of writing just numbers compared in smallest integral units with a sign of colon, : in between the two compared numbers. Example: 12miles travelled in 6hours indicates the ratio of distance in miles  to hours as 12:6 or 2:1 in smallest integral units, by dividing 12 and 6 by the HCF, 6.

Therefore, the ratio of miles to travel time in hours in the give problem is 180 : 4 or

180/4  : 1 or

45  : 1 .

Travelled miles : time in hour = 45:1.