Question

Equations and Graphs of Rational Functions Precalculus 12

Answer 1

Answer:

The average speed of the car is 90 km/h

Step-by-step explanation:

The rule of the distance id D = v × t, where

• v is the speed

• t is the time

∵ A car can travel 450 km in the same time it takes a train to travel

   350 km

→ That means the time of them are equals

∴ Time of the car = Time of the train

→ From the rule above t = $\frac{D}{v}$

∵ D(car) = 450 km and D(train) = 350 km

∵ The car's average speed is 20 km/h faster than the average speed

   of the train

→ Assume that the average speed of the train is x km/h

∴ v(train) = x km/h and v(car) = (x + 20) km/h

→ Use the rule of the time above to find the time of each one

∵ t(car) = $\frac{450}{(x+20)}$

∵ t(train) = $\frac{350}{x}$

∵ t(car) = t(train)

∴ $\frac{450}{(x+20)}$ =  $\frac{350}{x}$

→ By using cross multiplication

∵ 450 × x = 350 × (x + 20)

∴ 450x = 350(x) + 350(20)

∴ 450x = 350x + 7000

→ Subtract 350x from both sides

∴ 100x = 7000

→ Divide both sides by 100 to find x

∴ x = 70

∵ x represents the average speed of the train

∴ The average speed of the train = 70 km/h

∵ The average speed of the car = x + 20

∴ The average speed of the car = 70 + 20

∴ The average speed of the car = 90 km/h