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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 - Mathematics

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#### 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 1

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

#### Solution 2

The distance by road between A and B = 216km
and the distance by rail = 208km
speed of car = x km/hr
and speed of train = (x + 16)km/hr.

(i) Time taken by car = (216)/x"hours"

(ii) Time taaken by train = (208)/(x + 16)"hours".
(iii) According to the condition,

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

⇒ (216x + 3456 - 208x)/(x(x + 16) = 2

⇒ (8x + 3456)/(x^2 + 16x) = (2)/(1)

⇒ 8x + 3456 = 2x2 + 32x
⇒ 2x2 + 32x - 8x - 3456 = 0
⇒ 2x2 + 24x - 3456 = 0
⇒ x2 + 12x - 1728 = 0   ...(Dividing by 2)
⇒ x2 + 48x - 36x - 1728 = 0
⇒ x(x + 48) -36(x - 48) = 0
⇒ (x + 48)(x -36) = 0
Either x + 48 = 0,
then x = -48,
which is not possible as it is negative.
or
x - 36 = 0,
then x = 36.
(iv) Speed of the train
= (x + 16)km/hr.
= (36 + 16)km/hr.
= 52km/hr.

Is there an error in this question or solution?

#### APPEARS IN

Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(E) | Q: 1 | Page no. 78
ML Aggarwal Solution for Class 10 Mathematics (2016 (Latest))
Chapter 5: Quadratic Equations in One Variable
Exercise 5.5 | Q: 29