Rates And Ratios

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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 100 miles in 2 hours. Another vehicle B covers 90 miles in 3 hours. Find who travels faster.

A travels with the speed (distance per time ratio i.e. miles travelled per hour) = 100 miles/ 2 hours = 50 miles/ hours.

B travels with the speed (distance per time ratio i.e. miles travelled per hour) = 90 miles/ 3 hours = 30 miles/ hours.

Comparing the speeds, miles / hour ratio for A and B i.e. 50 miles / hour and 30 miles / hours gives A has greater speed.

Hence A has greater speed = 50 miles/hour.
 
Example 2: Sam can cycle a distance of 16 miles in 2 hours. Ben can covers 21 miles in 3 hours by cycling. Find who travels faster.

Sam travels with the speed (distance per time ratio i.e. miles travelled per hour) = 16 miles/ 2 hours = 8 miles/ hours.

Ben travels with the speed (distance per time ratio i.e. miles travelled per hour) = 21 miles/ 3 hours = 7 miles/ hours.

Comparing the cycling speeds for Sam and Ben.

Hence Sam has greater speed = 8 miles/hour.
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