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
∵ 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 = [tex]\frac{D}{v}[/tex]
∵ 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) = [tex]\frac{450}{(x+20)}[/tex]
∵ t(train) = [tex]\frac{350}{x}[/tex]
∵ t(car) = t(train)
∴ [tex]\frac{450}{(x+20)}[/tex] = [tex]\frac{350}{x}[/tex]
→ 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
