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 :
(i) the onward journey;
(ii) 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

Step-by-step explanation:

Given,

Distance = 400 km

Average speed of the aeroplane = x km/hr

And, speed while returning = (x+40) km/hr

We know that,

Time = Distance / Speed

(i) Time taken for onward journey = 400/x hrs

(ii) Time taken for return journey = 400/(x+40) hrs

Then, according to the question

x

400

−

x+40

400

=

60

30

x(x+40)

400x+16000−400x

=

2

1

x(x+40)

16000

=

2

1

x

2

+40x−32000=0

x

2

+200x−160x−32000=0

x(x+200)−160(x+200)=0

(x+200)(x−160)=0

So, x=−200 or 160

As the speed cannot be negative, x = 160 is only valid.