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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. - ICSE Class 10 - Mathematics

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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.

Solution

Let the speed of the car be x km/hr.

Distance = 36 km

Time taken to cover a distance of 36 km = 36/x hrs

(Time = Distance/Speed)

New speed of the car = (x + 10) km/hr

New time taken by the car to cover a distance of 36 km = 36/(x + 10) hrs

From the given information, we have:

`36/x - 36/(x + 10) = 18/60`

`(36x + 360 - 36x)/(x(x + 10)) = 3/10`

`360/(x^2 + 10x) = 3/10`

`120/(x^2 + 10x) = 1/10`

`x^2 + 10x - 1200 = 0`

(x + 40)(x - 30) = 0

x = -40,30

But speed cannot be negative So x = 30

Hence the original speed of the car is 30 km/hr

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 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: 2
Solution 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. Concept: Quadratic Equations.
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