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 the expression for the time taken for
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

TIme taken for the onward journey = `(400)/(x + 40)"hours"`.
According to the question,
`(400)/(x + 40) = (400)/x -(1)/(2)`

⇒ 800x = 800 (x + 40) - x(x + 40)

⇒  x² + 40x - 32,000 = 0

⇒  x² + 200x - 160x - 32000 = 0

⇒ x (x + 200) - 160 (x + 200) = 0

⇒  x = -200 (inadmissible) or 160

Hence, the required value of x is 160.