Question: An aeroplane first flew with a speed of 440 km/h and covered a certain distance. It still had to cover 770 km less than what it had already covered, but it flew with a speed of 660 km/h. The average speed for the entire flight was 500 km/h. Find the total distance covered.
Options:
A) 3250 km
B) 2750 km
C) 4400 km
D) 1375 km
Show Answer
Answer:
Correct Answer: B
Solution:
- Let x be the first lap of the flight,
Then, the second lap will be $ (x-770)km. $
Total distance $ =(2x-770)km $
Let be the total time of journey
$ \Rightarrow $ $ \frac{x}{440}+(x-770)/660=t $
(i)
$ 500t=2x-770 $
(ii)
From Eq. (i),
$ 660x+440x-770\times 440=660\times 440t $
$ \Rightarrow $ $ 6x+4x-770\times 4=6\times 440t $
$ \Rightarrow $ $ 6x+4x-3080=2640t $
$ \Rightarrow $ $ 3x+2x-1540=1320t $
(iii)
From Eq. (ii),
$ 2x-770=500t $
(iv)
On subtracting Eqs. (iii) and (vi), we get
$ 3x-770=820t $
(v)
From Eqs. (iv) and (v), (v) and (iv), then $ x=320t $
Putting the value of x in Eq. (iii), we have
$ 5\times 320t-1540=1320t $
$ \Rightarrow $ $ 280t=1540 $
$ \Rightarrow $ $ t=5.5 $
$ \Rightarrow $ $ x=320\times 5.5=1760 $
Total distance
$ =2x-770=2\times 1760-770=2750km $
BETA
