Question

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 xkm/hr whereas a train starts from station B with a speed 20km/hr more than the speed of the car?
(i)The time taken by car to reach station B is
(a) 240(b) 300(c) 20(d) 300+20
(ii) The time taken by train to reach station A
(a) 240 (b) 300 (c) 20 (d) 300+20
(iii)If the time taken by train is 1 hour less than that taken by the car, then the quadratic equation formed is (a) x2+ 80x –6000=0 (b) x2+ 80x –4800=0 (c) x2+ 240x -1600 =0 (d) x2-80x +4800 = 0 (iv)The speed of the car is(a) 60km/hr (b) 120km/hr (c) 40km/hr (d) 80km/hr

Answer 1

Answer:

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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 the quadratic equation formed

(iv)The speed of the car

Solution: Speed of car= x km/h

Speed of train = x+20 km/h

Distance travelled by car= 240 km

Distance travelled by train= 300 km

Time taken by car

= Distance travelled by car / Speed of car

= 240/x

Time taken by train

= Distance travelled by train / Speed of train

= 300/x+20

Time taken by train is one hour less than time taken by car, therefore:

Time taken by car- Time taken by train= 1

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

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

$= > \frac{240x + 4800 - 300x}{ {x}^{2} + 20x} = 1$

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

$= > {x}^{2} + 20x + 60x - 4800 = 0$

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

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

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

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

=> x = -120 or x =40

But speed cannot be negative, therefore x= 40

Speed of car = 40 km/h

Time taken by car

= 240/40

= 6 hours

Speed of train = x+20 = 60 km/h

Time taken by car

= 300/60

= 5 hours

Therefore,

(i) Time taken by car to reach station B is 6 hours

(ii) Time taken by train to reach station A is 5 hours

(iii) The equation formed if time taken by train is one hour less than time taken by car is option (b) ${x}^{2} + 80x - 4800 = 0$

(iv) The speed of car is option (c) 40 km/h.