Question

An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey, the speed was increased by 40 km/hr. Write down an expression for the time taken for:

1. the onward journey;
2. the return journey.

If the return journey took 30 minutes less than the onward journey, write down an equation in x and find its value.

Answer 1

Distance = 400 km

Speed of aeroplane = x km/hr

i. ∴ Time taken = `(400)/x` hours

On increasing the speed by 40 km/hr,

On the return journey, the speed = (x + 40) km/hr.

ii. Time taken = `(400)/(x + 40)"hours"`

Now according to the condition,

`(400)/x - (400)/(x + 40) = 30  "minutes" = (1)/(2)`

`400[(1)/x - (1)/(x + 40)] = (1)/(2)`

`\implies 400[(x + 40 - x)/(x(x + 40))]`

`\implies (400 xx 40)/(x^2 + 40x) = (1)/(2)`

`\implies` x² + 40x = 400 × 40 × 2

`\implies` x² + 40x – 32000 = 0

`\implies` x² + 200x – 160x – 32000 = 0

`\implies` x(x + 200) – 160(x + 200) = 0

`\implies` (x + 200)(x – 160) = 0

Either x + 200 = 0,

Then x = –200,

Which is not possible as it is negative.

or

x – 160 = 0,

Then x = 160.