A car moves a distance of 200 m. It covers the first half of the distance at speed 40 km/h and second half of the distance at speed v. The average speed is 48 km/h. The value of v is
(1) 56 km/h
(2) 60 km/h
(3) 50 km/h
(4) 58 km/h
Answers
Given :-
◉ A car moves a distance of 200 m.
◉ The car covers the first half of the distance at speed 40 km/h and second half of the distance at speed v.
◉ Average speed is 48km/h
To Find :-
◉ Value of v
Solution :-
Since we are given the total distance travelled hy the car i.e., 200 m. So, we just have to find the total time taken.
Case 1
It is given that the car covered half of the distance with speed 40 km/h
We have,
Speed = 40 km/h
Distance = 200/2 ⇒ 100 m or 0.1 Km
We know,
⇒ Distance = Speed × Time
⇒ 0.1 = 40 × t₁
⇒ t₁ = 1/400 ...(1)
Case 2
Also, The car covered next half of the distance with speed v, we have
Distance travelled = 100 m or 0.1 km
Speed = v km/h
We know,
⇒ Distance = Speed × Time
⇒ 0.1 = v × t₂
⇒ t₂ = 1/10v ...(2)
Now, It is given that the average speed of the car is 48 km /hr , we have
Total distance travelled = 200 m or 0.2 km
Total time taken = t₁ + t₂
⇒ Average speed = Total distance / Total time
⇒ 48 = 0.2 / (t₁ + t₂)
⇒ 48 / 0.2 = 1 / (1/400 + 1/10v)
⇒ 240 = 1 / { (v + 40)/400v }
⇒ 240 = 400v / (v + 40)
⇒ 240v + 9600 = 400v
⇒ 160v = 9600
⇒ v = 60 km/h
Hence, The value of v is 60 km/h
∴ Option (2) is correct.
Answer:
We have given the speed of the car in the first half is v1=40km/hr and the average speed of the car in the total journey is vavg=48km/hr. Therefore, the correct answer is option D.