#### 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