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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. - ICSE Class 10 - Mathematics

#### 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 the original speed of the car = x km/h

Distance covered = 400 km

Time taken = "Distance"/"Speed" = 400/x hours

If the speed is increased by 12 km/h the time taken = "Distance"/"Speed" = 400/(x + 12) hours

According to question,

400/x - 400/(x + 12) = "1 hour 40 min" = 1 40/60 minutes

=> 400(1/x - 1/(x + 12)) = 5/3

=> (x + 12 - x)/(x(x + 12)) = 5/(3 xx 400)

=> 12/(x(x + 12)) = 1/240

=> x^2 + 12x - 2880 = 0

=> (x - 48)(x + 60) = 0

=> x = 48, -60

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

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

Is there an error in this question or solution?

#### APPEARS IN

Selina Solution for Selina ICSE Concise Mathematics for Class 10 (2018-2019) (2017 to Current)
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Ex.6C | Q: 4
2011-2012 (March) (with solutions)
Question 9.3 | 4.00 marks

#### Video TutorialsVIEW ALL [5]

Solution 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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