An aeroplane travels a distance of 17,644 km in 22 hours. Calculate the
distance travelled by a plane per hour if it covers same distance every hour.
Answers
Answer:
Hey There!!
Here we can see that one thing remains constant in both forward and return journey:
Distance of the journey = 400 km
On the first journey,
Average Speed = x km/hr
We know that:
\begin{gathered}Speed = \frac{Distance}{Time} \\ \\ v=\frac{d}{t} \\ \\ \implies t=\frac{d}{v} \\ \\ \implies \boxed{t_1=\frac{400}{x}\,\,hours}\end{gathered}
Speed=
Time
Distance
v=
t
d
⟹t=
v
d
⟹
t
1
=
x
400
hours
On the return journey, Average Speed was increased by 40 km/hr.
So, we have:
\begin{gathered}x+40=\frac{400}{t_2} \\ \\ \\ \implies \boxed{t_2=\frac{400}{x+40}}\end{gathered}
x+40=
t
2
400
⟹
t
2
=
x+40
400
We are given that the return journey took 30 minutes less than the onward journey. So we can say that the time difference is half an hour.
\begin{gathered}t_1-t_2 = \frac{1}{2} \, \, hours \\ \\ \\ \implies \frac{400}{x} - \frac{400}{x+40} = \frac{1}{2} \\ \\ \\ \implies 400 \left(\frac{1}{x}-\frac{1}{x+40}\right)=\frac{1}{2} \\ \\ \\ \implies 800 (x+40 - x) = x(x+40) \\ \\ \\ \implies x^2+40x-32000=0 \\ \\ \\ \implies x^2+200x-160x-32000=0 \\ \\ \\ \implies x(x+200)-160(x+200)=0 \\ \\ \\ \implies (x+200)(x-160)=0 \\ \\ \\ \implies x=-200 \, \, OR \, \, x=160 \end{gathered}
t
1
−t
2
=
2
1
hours
⟹
x
400
−
x+40
400
=
2
1
⟹400(
x
1
−
x+40
1
)=
2
1
⟹800(x+40−x)=x(x+40)
⟹x
2
+40x−32000=0
⟹x
2
+200x−160x−32000=0
⟹x(x+200)−160(x+200)=0
⟹(x+200)(x−160)=0
⟹x=−200ORx=160
Since average speed cannot be negative, we have:
\boxed{x=160\,\,km / hr}
x=160km/hr
___________________________________________
So, finally your answers are:
(1)\,\,t=\frac{400}{x}\,hr(1)t=
x
400
hr
(2)\,\,t=\frac{400}{x+40}\,hr(2)t=
x+40
400
hr
\begin{gathered}(3)\,\textrm{The equation is: }x^2+40x-32000=0 \\ \\ \\and \, \, x=160\,km / hr\end{gathered}
(3)The equation is: x
2
+40x−32000=0
andx=160km/hr
Hope it helps
shalinisachan
Brainly Community