Question

solve the equation of quadratic

Answer 1

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Answer 2

Distance = 600 km

Speed = x km/h

Time = Distance ÷ Speed

Time = 600/x hours

Distance = 600 km

Speed = (x + 20) km/h

Time = Distance ÷ Speed

Time = 600/(x + 20) hours

Solve x:

The difference in time is 5 hours

600/x - 600/(x + 20) -   = 5

Put into single fraction:

[ 600(x + 20) - 600x ] /x(x + 20) = 5

Cross-multiply:

600(x + 20) - 600x = 5x(x + 20)

Expand:

600x + 12000 - 600x = 5x² + 100x

Combine like terms:

5x² + 100x - 12000 = 0

Divide by 5:

x² + 20x - 2400= 0

Factorise:

(x - 40)(x + 60) = 0

Apply zero product property:

x = 40 or x = - 60 (rejected)

Answer: x = 40