Question : A car left 3 minutes earlier than the scheduled time and to reach the destination 126 km away in time, it has to slow its speed by 6 km/hr from the usual. What is the usual speed (in km/hr) of the car?
Option 1: 56
Option 2: 63
Option 3: 94.5
Option 4: 126
Correct Answer: 126
Solution :
Let the usual speed be $x$ km/hr.
According to the question,
$\frac{126}{x}-\frac{126}{x-6}=\frac{3}{60}$
$⇒\frac{252}{x^2-6x}=\frac{1}{60}$
$⇒x^2-6x-15120=0$
$⇒x^2-(126-120)x-15120=0$
$⇒(x-126)(x+120)=0$
As speed can't be negative,
$\therefore x= 126$ km/hr
Hence, the correct answer is 126.
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