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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 t - ICSE Class 10 - Mathematics

Question

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:
(1) the time is taken by the car to reach town B from A, in terms of x;
(2) the time is taken by the train to reach town B from A, in terms of x.
(3) If the train takes 2 hours less than the car, to reach town B, obtain an equation in x and solve it.
(4) Hence, find the speed of the train.

Solution

Speed of car = x  km/hr

Speed of train = (x + 16) km/hr

1) we know Time = "Distance"/"Speed"

Time is taken by the car to reach town B From A = 216/x hrs

2) Time taken by the train to reach town B from A = 208/(x + 16) hrs

3) From the given information

216/x - 208/(x + 16) = 2

(216x + 3456 - 208x)/(x(x + 16)) = 2

(8x + 3456)/(x(x + 16)) = 2

4x + 1728 = x^2  + 16x

x^2 + 12x - 1728 = 0

x^2 + 48x - 36x - 1728 = 0

x(x + 48)- 36(x + 48) = 0

(x + 48)(x - 36) = 0

x = -48, 36

But speed cannnot be negative  So x = 36

4) Speed of train = (36 + 16) km/ hr = 52 km/hr

Is there an error in this question or solution?

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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.6E | Q: 1

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Solution 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 t Concept: Quadratic Equations.
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