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A Car Covers a Distance of 400 Km at a Certain Speed. Had the Speed Been 12 Km/H More, the Time Taken for the Journey Would Have Been 1 Hour 40 Minutes Less. Find the Original Speed of the Car. - Mathematics

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Question

A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.

Solution

Let x km/h be the original speed of the car.

We know that,

Time taken = `"Distance"/"Speed"`

It is given that the car covers a distance of 400 km with the speed of x km/h.

Thus, the time taken by the car to complete 400 km is

t = `400/"x"`

Now, the speed is increased by 12 km.
Increased speed = (x + 12) km/h

Also given that, increasing the speed of the car will decrease the time taken by 1 hour 40 minutes.
Hence,

`400/"x" - 400/("x" + 12)` = 1 hour 40 minutes

⇒ `400/"x" - 400/("x" + 12)` = `1 40/60`

⇒ `(400 ("x" + 12) - 400"x")/("x"("x" + 12)) = 1 2/3`

⇒ `(400"x" + 4800 - 400"x")/("x"("x" + 12)) = 5/3`

⇒ `4800/("x"("x" + 12)) = 5/3`

⇒ 3 x 4800 = 5 × x × (x + 12)
⇒ 14400 = 5x2 + 60x
⇒ 5x2 + 60x - 14400 = 0
⇒  x2 + 12x - 2880 = 0
⇒ x2 + 60x - 48x - 2880 = 0
⇒ x (x + 60) - 48 (x + 60) = 0
⇒ ( x + 60) ( x - 48) = 0
⇒ x + 60 = 0 or x - 48 = 0
⇒ x = -60 or x = 48

Since, speed cannot be negative, we reject -60.

Hence, the original speed of the car is 48 km/h.

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A Car Covers a Distance of 400 Km at a Certain Speed. Had the Speed Been 12 Km/H More, the Time Taken for the Journey Would Have Been 1 Hour 40 Minutes Less. Find the Original Speed of the Car. Concept: Quadratic Equations.
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