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Solving a Quadratic Equation by Factorization Method

If the speed ...

Question

If the speed of a car is increased by 10 km per hr, it takes 18 minutes less to cover a distance of 36 km. Find the speed of the car.

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Solution

Let the speed of the car be x
time taken to cover 36 km = 36/x hr
According to question

$36 over x minus fraction numerator 36 over denominator x plus 10 end fraction equals 18 over 60 fraction numerator 36 left parenthesis x plus 10 right parenthesis minus 36 x over denominator x left parenthesis x plus 10 right parenthesis end fraction equals 3 over 10 3600 over blank equals 3 x squared plus 30 x x squared plus 30 x minus 3600 equals 0$

x(x+40) - 30(x+ 40)= 0
(x-30)(x+40)=0
we get 2 answers
But x=30 is the correct one
therefore the speed of the car is 30 km/hr

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