Question

In a flight of 2800 km, an aircraft was slowed down due to bad weather. its average speed is reduced by 100km/h and time increased by 30 mins. find the original duration.

Answer 1

speed of aircraft= x
Distance = 2800 km

Time = Distance / Speed = 2800/x 
Given:

The speed has reduced by 100 and time is reduced by 30 min

New speed = (x – 100)
That is, 30 min = 30/60 hr = (1/2) hr 
Time taken= 2800/(x – 100) hr
=2800/(x – 100)

= (2800/x) + (1/2)
2800/(x-100) -` (2800/x)  =  1/2

x² - 100x - 560000  = 0

x² - 800x + 700x - 560000  =  0

x(x - 800) + 700(x - 800)  =  0
(x + 700) (x - 800)  =  0
SO,

x  =  - 700 or 800

Thus original duration of the flight =  2800/800 = 7/2 hours
OR = 3 hr 30 mins

Answer 2

▶ Answer :-

→ The original duration of the flight = 3 hours 30 minutes .

▶ Step-by-step explanation :-

→ Let the original speed of the aircraft be x km/hr .

→ Time taken to cover 2800 km = $\frac{2800}{x}$ hours .

→ Reduced speed = ( x - 100 ) km/hr .

→ Time taken to cover 2800 km at this speed = $\frac{2800}{x - 100 }$ hours .

$\huge \pink { \mid{ \underline{ \overline{ \tt Solution :- }} \mid}}$

▶ Now,

$\begin{lgathered}\sf \therefore \frac{2800}{(x - 100)} - \frac{2800}{x} = \frac{30}{60} . \\ \\ \sf \implies \frac{1}{(x - 100)} - \frac{1}{x} = \frac{1}{2 \times 2800} . \\ \\ \sf \implies \frac{x - (x - 100)}{(x - 100)x} = \frac{1}{5600} . \\ \\ \sf \implies \frac{100}{( {x}^{2} - 100x) } = \frac{1}{5600} . \\ \\ \sf \implies {x}^{2} - 100x - 560000 = 0. \\ \\ \sf \implies {x}^{2} - 800x + 700x - 560000 = 0. \\ \\ \sf \implies x(x - 800) + 700(x - 800) = 0. \\ \\ \sf \implies (x - 800)(x + 700) = 0. \\ \\ \sf \implies x - 800 = 0. \: \: \green{or} \: \: x + 700 = 0. \\ \\ \sf \implies x = 800. \: \: \green{or} \: \: x = - 700. \\ \\ \huge{ \orange{ \boxed{ \boxed{ \sf \implies x = 800.}}}} \\ \\ \bigg[ \tt \because speed \: cannot \: be \: negative. \bigg]\end{lgathered}$

•°• Original speed of the aircraft = 800 km/hr .

And, original duration of the flight = $\frac{2800}{800}$ hours = 3 hours 30 minutes .

✔✔ Hence, it is solved ✅✅.