Question

23.
The distance between station A and B by road is 240 km and by train it is 300 km. A car starts from station A with a speed x km/hr whereas a train starts from station B with a speed 20km/hr more than the speed of the car. find
(i)The time taken by car to reach station B
(ii)The time taken by train to reach station A
(iii)If the time taken by train is 1 hour less than that taken by the car, then find the quadratic equation formed
(iv)The speed of the car

show the working not only answer

Answer 1

Answer:

(i) 240/x

(ii) 300/x+20

(iii) x²+80x-4800=0

(iv) 40 km/h

Step-by-step explanation:

(i) Speed= distance/time.

=240/x

(ii) speed = distance/time

=300/x+30

(iii) speed of car-speed of train = 1

(240/x) - (300/x+20) = 1

simplify this equation step by step-----

240x+4800-300x=x²+20x

-x²-80+4800=0

x²+80-4800=0

(iv) solve the above equation for x.

x²+80-4800=0

x²+120x-40x-4800=0

x(x+120) -40(x+120)

(x-40)(x+120)

x=40           x= -120

answer cant be in negative.

So, x= 40km/h

Answer 2

Given: The distance between station A and B by road is 240 km and by train it is 300 km. A car starts from station A with a speed x km/hr whereas a train starts from station B with a speed 20km/hr more than the speed of the car.

To find: (i)The time taken by car to reach station B

(ii)The time taken by train to reach station A

(iii)If the time taken by train is 1 hour less than that taken by the car, then find the quadratic equation formed

(iv)The speed of the car

Solution: Here, speed of the car= x km/h

Since speed of train is 20km/h more than the speed of the car, therefore speed of car= (x+20) km/h

Now, time taken to complete a distance

= Total distance covered/ Speed of the body

Time taken by car

= Distance covered by car/ Speed of car

= 240/x

Time taken by train

= Distance covered by train/ Speed of train

= 300/ x+20

Since time taken by train is one hour less than the time taken by the car, the equation that can be formed is:

Time taken by car - time taken by train = 1

$= > \frac{240}{x} - \frac{300}{x + 20} = 1$

$= > \frac{240(x + 20) - 300x}{x(x + 20)} = 1$

$= > 240x + 4800 - 300x = x(x + 20)$

$= > - 60x + 4800 = {x}^{2} + 20x$

$= > {x}^{2} + 80x - 4800 = 0$

$= > {x}^{2} + 120x - 40x - 4800 = 0$

$= > x(x + 120) - 40(x + 120) = 0$

=> (x+120) (x-40)= 0

=> x+120 = 0 or x-40=0

=> x= -120 or x= 40

Since speed cannot be negative, therefore x= 40

Using x=40

Time taken by car

= 240/x

= 240/40

= 6 hours

Time taken by train

= 300/x+20

= 300/60

= 5 hours

Therefore,

Time taken by car = 6 hours

Time taken by train= 5 hours

The quadratic equation formed

$= {x}^{2} + 80x - 4800$

Speed of car= 40 km/h