Saved Bookmarks
| 1. |
In a flight of 600 km an aircraft was slowed down due to bad weather. Its average speed was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is;1. 1hr2. 2 hrs3. 3 hrs4. 4 hrs |
|
Answer» Correct Answer - Option 1 : 1hr Given: Total Distance = 600 km. average speed was reduced = 200 km/hr the time of flight increased = 30 minutes Formula Used: ∵ Average Speed = Total Distance / Time Calculations: Let, the original duration of flight be t hrs. So, original average speed = 600/t Due to bad weather speed of trip is reduced by 200 km/hr and time of flight is increased by 30 minutes i.e. 0.5 hr. ∴ Reduced average speed = (600/t) – 200 And New duration of flight = (t + 0.5) hrs So, the new average speed = 600/(t + 0.5) Equating, \(\begin{array}{l} \Rightarrow \frac{{600}}{t}-200 = \frac{{600}}{{t + 0.5}}\\ \Rightarrow \frac{3}{t}-1 = \frac{3}{{t + 0.5}}\\ \Rightarrow \frac{{3-t}}{t} = \frac{3}{{t + 0.5}} \end{array}\) ⇒ t2 + 0.5t – 1.5 = 0 ⇒ 2t2 + t – 3 = 0 ⇒ 2t2 – 2t + 3t – 3 = 0 ⇒ (t – 1)(2t + 3) = 0 ⇒ (t – 1) = 0 ∴ t = 1 hr ∴ The duration of the flight is 1 hr. |
|