If the speed of an aeroplane is decreased by 120 km/h, it takes 18 minutes more
to travel some distance. If the speed is increased by 180 km/h, it takes 18 minutes
less to travel the same distance. Find the average speed of the aeroplane and the
distance
Answers
Answer:
Required formula:
Average Speed =
Let the average speed of the aeroplane be denoted by “x” km/hr and the distance travelled by it be denoted by “y” km/hr.
Step 1:
According to the first condition given in the question and based on the above formula, we can write the eq. as,
⇒ …… (i)
According to the second condition given in the question and based on the above formula, we can write the eq. as,
⇒ …… (ii)
Step 2:
On dividing the eq. (i) by (ii), we get
⇒
⇒
⇒ 120 (x+180) = 180 (x-120)
⇒ 2x + 360 = 3x - 360
⇒ x = 720 km/hr
Step 3:
Substituting the value of x = 720 km/hr in eq. (i), we get
⇒
⇒
⇒ y =
⇒ y = 1080 km
Thus, the average speed of the car is 720 km/hr and the distance travelled by it is 1080 km.
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Answer:
720 km/hr and 1080 km
Step-by-step explanation:
Let its average speed = x km/hr and distance = y km.
We have two conditions here.
Condition 1 :
If the speed of an aeroplane is decreased by 120 km/h, it takes 18 minutes more to travel some distance.
=> (y/x - 120) - y/x = 18/60
=> y * [1/(x - 120) - 1/x] = 18/60
Condition 2 :
If the speed is increased by 180 km/h, it takes 18 minutes less to travel the same distance.
=> (y/x) - (y/x + 180) ] = 18/60
=> y * [1/x - 1/x + 180] = 18/60
Solve 1 and 2 conditions, we will get
=> (1/x - 120) - 1/x = 1/x - 1/x + 180
=> 120(x + 180) = 180(x - 120)
=> x = 720 km/hr
Place x in condition (1).
=> y * (1/(720 - 120) - 1/720] = 18/60
=> y[1/600 - 1/720] = 18/60
=> y = 1080 km
Hence,
Average Speed = 720 km/hr and Distance = 1080 km.
#Hope my answer helped you!