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# A Girl Goes to Her Friend’S House, Which is at a Distance of 12 Km. She Covers Half of the Distance at a Speed of X Km/Hr and the Remaining Distance at a Speed of (X + 2) Km/Hr. If She Takes 2 - ICSE Class 10 - Mathematics

#### Question

A girl goes to her friend’s house, which is at a distance of 12 km. She covers half of the distance at a speed of x km/hr and the remaining distance at a speed of (x + 2) km/hr. If she takes 2 hrs 30 minutes to cover the whole distance, find ‘x’.

#### Solution

We know

Time = Distance/Speed

Given the girl covers a distance of 6 km at a speed x km/hr

Time taken to cover first 6 km = 6/x

Also the girl covers the remaining 6 km distance at a speed (x + 2) km/hr.

Time taken to cover the whole distance = 2 hrs 30 mins - 2 30/60 = 2 1/2 = 5/2 hrs

∴ 6/x + 6/(x + 2) = 5/2

(6x + 12 + 6x)/(x(x + 2)) = 5/2

(12 + 12x)/(x^2 + 2x) = 5/2

24 + 24x = 5x^2 + 10x

5x^2 - 14x - 24 = 0

5x^2 - 20x + 6x - 24 = 0

5x(x - 4) + 6(x - 4) = 0

(5x + 6)(x - 4) = 0

x = (-6)/5, 4

Since speed cannot be negative. Therefore x = 4

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: 5

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Solution A Girl Goes to Her Friend’S House, Which is at a Distance of 12 Km. She Covers Half of the Distance at a Speed of X Km/Hr and the Remaining Distance at a Speed of (X + 2) Km/Hr. If She Takes 2 Concept: Quadratic Equations.
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