A train travels 360 km at a uniform speed. If the speed had been 5 km / hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Let the original speed of the train be x k m / h r . We can say that increased speed of the train will be ( 5 + x ) k m / h r . Time taken by the train to travel a distance of 360 km at a speed of x k m / h r = 360 x h r Time taken by the train to travel a distance of 360 km at a speed of ( 5 + x ) k m / h r = 360 x + 5 h r . ⇒ 360 x - 360 x + 5 = 1 ⇒ 360 x + 5 - 360 x x x + 5 = 1 ⇒ 360 x + 1800 - 360 x x 2 + 5 x = 1 ⇒ x 2 + 5 x = 1800 ⇒ x 2 + 5 x - 1800 = 0 Factorizing the quadratic equation by splitting the middle term, ⇒ x 2 - 40 x + 45 x - 1800 = 0 ⇒ x ( x - 40 ) + 45 ( x - 40 ) = 0 ⇒ ( x - 40 ) ( x + 45 ) = 0 ⇒ ( x - 40 ) = 0 ⇒ x = 40 or ⇒ ( x + 45 ) = 0 ⇒ x = - 45 Since the speed of the train can never be a negative value so, x = 40 . Thus, the original speed of the train is 40 k m / h r .

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A train travels at a certain average speed for a distance $63 km$ and then travels a distance of $72 km$ at an average speed of $6 km / hr$ more than the original speed. If it takes $3$ hours to complete total journey, what is its original average speed?

Important Questions on Quadratic Equations

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.8>Q 9

A train covers a distance of

90 km

at a uniform speed. Had the speed been

15 km / hour

more, it would have taken

30 minutes

less for a journey. Find the original speed of the train.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.8>Q 10

A train travels

360 km

at a uniform speed. If the speed had been

\Rightarrow (3 x + 9) (x - 42) = 0

more, it would have taken

1 hour

less for the same journey. Find the speed of the train.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.8>Q 11

An express train takes

1 hour

less than a passenger train to travel

132 km

between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is

11 km / hr

more than that of the passenger train, find the average speed of two trains.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.8>Q 12

An aeroplane left

50 minutes

later than its scheduled time, and in order to reach the destination,

1250 km

away, in time, it had to increase its speed by

250 km / hr

from its usual speed. Find its usual speed.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.8>Q 13

While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by

30

minutes to reach the destination,

1500 km

away in time, the pilot increased the speed by

100 km / hr

. Find the original speed/hour of the plane.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.8>Q 14

A motor boat whose speed in still water is

18 km / hr

takes

1

hour more to go

24 km

upstream than to return downstream to the same spot. Find the speed of the stream.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.8>Q 15

A car moves a distance of

2592 km

with uniform speed. The number of hours taken for the journey is one-half the number representing the speed, in

km / hour

. Find the time taken to cover the distance.

MEDIUM

10th CBSE

IMPORTANT

MATHEMATICS CLASS X>Chapter 4 - Quadratic Equations>EXERCISE 4.9>Q 1

Ashu is

x

years old while his mother Mrs.Veena is

x^{2}

years old. Five years hence Mrs.Veena will be three times old as Ashu. Find their present ages.

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed?

Important Questions on Quadratic Equations

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A train travels at a certain average speed for a distance $63 km$ and then travels a distance of $72 km$ at an average speed of $6 km / hr$ more than the original speed. If it takes $3$ hours to complete total journey, what is its original average speed?