Question

(1) 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.​

Answer 1

If the average speed decreases by 120 km/hr & the time increase by 18 min and if the speed is increased by 180 km/hr & the time reduces by 18 mins then the average speed of the car is  720 km/hr and the distance travelled is 1080 km.

Step-by-step explanation:

Required formula:

Average Speed = $\frac{Total Distance}{Total Time}$

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,

$\frac{y}{x-120} - \frac{y}{x} = \frac{18}{60}$

⇒ $y * [\frac{1}{x-120} - \frac{1}{x}] = \frac{18}{60}$ …… (i)

According to the second condition given in the question and based on the above formula, we can write the eq. as,

$\frac{y}{x} - \frac{y}{x+180} = \frac{18}{60}$

⇒ $y * [\frac{1}{x} - \frac{1}{x+180}] = \frac{18}{60}$ …… (ii)

Step 2:

On dividing the eq. (i) by (ii), we get

$\frac{1}{x-120} - \frac{1}{x}$ = $\frac{1}{x} - \frac{1}{x+180}$  

⇒ $\frac{</strong>x-x+120<strong>}{</strong>x(x-120)<strong>}$ = $\frac{</strong>x+180-x<strong>}{</strong>(x+180)x<strong>}$

⇒  $\frac{</strong>120<strong>}{</strong>x(x-120)<strong>}$ = $\frac{</strong>180<strong>}{</strong>(x+180)x<strong>}$

⇒ 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 [$\frac{1}{720-120} - \frac{1}{720}$] = $\frac{18}{60}$

⇒ y [$\frac{1}{600} - \frac{1}{720}$] = $\frac{3}{10}$

⇒ y [$\frac{720 - 600}{720*600}$] = $\frac{3}{10}$

⇒ y = $\frac{3}{10}$  * (720*600) * $\frac{1}{120}$

⇒ y = 1080 km

Thus, the average speed of the car is 720 km/hr and the distance travelled by it is 1080 km.

----------------------------------------------------------------------------------

Also View:

It took a car 6 hours to cover the distance between points A and B with the speed of 50mp/h. How long will it take a bus to cover the same distance, if it travels at 40mp/h?

https://brainly.in/question/13203194

Tracey ran to the top of a steep hill with an average pace of 6 miles per hour she took the exact same trail back down. to her relief the decend was much faster. the average speed rose to 14 miles per hour if entire journy took tracey 1 hour to complete and she did not stop anywhere what is the length of the trail in miles in miles one way.

https://brainly.in/question/8218417

It took a car 6 hours to cover the distance between points A and B with the speed of 50mp/h. How long will it take a bus to cover the same distance, if it travels at 40mp/h?

https://brainly.in/question/13203194

Answer 2

Answer:

Iska answer photo me hai...

Idhar nahi upar photo me dekhna honga....

Answer photo me dekho...

Photo me hi answer hai...

Answer dekho...