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 taken by the car to reach town B from A, in terms of x;
2. the time 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.

Answer 1

Speed of car = x km/hr

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

i. We know: Time = `"Distance"/"Speed"`

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

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

iii. 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 = x² + 16x

x² + 12x – 1728 = 0

x² + 48x – 36x – 1728 = 0

x(x + 48) – 36(x + 48) = 0

(x + 48)(x – 36) = 0

x = – 48, 36

But, speed cannot be negative. 

So, x = 36.

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