# Ratios and Rates

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Rates ratio is one of the very useful concept in Math. The rate is defined as the ratio between two different quantities. Ratio is the quantitative comparison between the given quantities. Therefore the rate ratio is where two different quantities are compared. Some examples for the rate ratio are centimeter per minute written as cm/min; kilometers per second written as km/sec.

Example 1: A vehicle A can cover a distance of 50 miles in 2 hours. Another vehicle B covers 45 miles in 3 hours. Find who travels faster.

A travels with the speed (distance per time ratio i.e. miles travelled per hour) = 50 miles/ 2 hours = 25 miles/ hours.

B travels with the speed (distance per time ratio i.e. miles travelled per hour) = 45 miles/ 3 hours = 15 miles/ hours.

Comparing the speeds, miles / hour ratio for A and B i.e. 25 miles / hour and 15 miles / hours gives A has greater speed.

Hence A has greater speed = 25 miles/hour.

Example 2: Jack can cycle a distance of 18 miles in 3 hours. John can covers 28 miles in 4 hours by cycling. Find who travels faster.

Jack travels with the speed (distance per time ratio i.e. miles travelled per hour) = 18 miles/ 3 hours = 6 miles/ hours.

John travels with the speed (distance per time ratio i.e. miles travelled per hour) = 28 miles/ 4 hours = 7 miles/ hours.

Comparing the cycling speeds for Jack and John.

Hence John has greater speed = 7 miles/hour.