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The distance by road between two towns A and B is 216 km, and by rail it is 208 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. Calculate: (iii) If the train takes 2 hours less than the car, to reach town B, obtain an equation in x and solve it. (iv) Hence, find the speed of the train.
The distance by road between two towns A and B is 216 km, and by rail it is 208 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. Calculate: (iii) If the train takes 2 hours less than the car, to reach town B, obtain an equation in x and solve it. (iv) Hence, find the speed of the train.
Class 10 | Exercise 6E | ICSE | Maths | Selina | Solving (simple) Problems (Based on Quadratic Equations)
The distance by road between two towns A and B is 216 km, and by rail it is 208 km. A car travels at a speed of x km/hr and the train travels at a speed which is 16 km/hr faster than the car. Calculate: (iii) If the train takes 2 hours less than the car, to reach town B, obtain an equation in x and solve it. (iv) Hence, find the speed of the train.

(iii) According to the question,

Concise Selina Solutions Class 10 Maths Chapter 6 ex. 6(E) - 1

\[4x\text{ }+\text{ }1728\text{ }=\text{ }{{x}^{2}}~+\text{ }16x\]

Or,

\[{{x}^{2}}~+\text{ }12x\text{ }\text{ }1728\text{ }=\text{ }0\]

Or,

\[{{x}^{2}}~+\text{ }48x\text{ }\text{ }36x\text{ }\text{ }1728\text{ }=\text{ }0\]

Or,

\[x\left( x\text{ }+\text{ }48 \right)\text{ }\text{ }36\left( x\text{ }+\text{ }48 \right)\text{ }=\text{ }0\]

Or,

\[\left( x\text{ }+\text{ }48 \right)\text{ }\left( x\text{ }\text{ }36 \right)\text{ }=\text{ }0\]

Or,

\[x\text{ }=\text{ }-48,\text{ }36\]

As speed cannot be negative,

\[x\text{ }=\text{ }36\]

(iv) Therefore, the speed of the train is:

\[~\left( x\text{ }+\text{ }16 \right)\text{ }=\text{ }\left( 36\text{ }+\text{ }16 \right)km/hr\text{ }=\text{ }52\text{ }km/h\]

i

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