a train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. if it takes 3 hours to complete the total journey, what is its first speed?

get a train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. if it takes 3 hours to complete the total journey, what is its first speed? from screen.

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

Byju's Answer Standard X Mathematics

Solving Using Quadratic Formula When D>0

A train trave... Question

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

Open in App Solution Distance = 54 km

Let the average speed be x

Distance= 63km

The average speed to cover this distance = x+6

Total Time Taken= 3 hr.

D/S =t

therefore, 54/x + 63/x+6 = 3

54(x+6) +63x =3x(x+6)

3 x 2 − 99 x − 324 =0 x=36, -3 Hence x= 36km/hr Suggest Corrections 57

SIMILAR QUESTIONS

Q. A train travels at a certain average speed of a distance of

63 k m

and then travels at a distance of

72 k m

at an average speed of

6 k m / h r

more than its original speeds. If it takes

3

hours to complete total journey, what is the original average speed?

Q. A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

OR

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

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A Train Travels at a Certain Average Speed for a Distanced of 54 Km and Then Travels a Distance of 63 Km at an Average Speed of 6 Km/Hr More than the First Speed.

A Train Travels at a Certain Average Speed for a Distanced of 54 Km and Then Travels a Distance of 63 Km at an Average Speed of 6 Km/Hr More than the First Speed.

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A train travels at a certain average speed for a distanced of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

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SOLUTION

Let the first speed of the train be x km/h

Time taken to cover 54km

=54xh

(Time=DistanceSpeed)

New speed of the train =

(x+6) km/h

∴ Time taken to cover 63km=

63x+6h

According to the given condition,

Time taken to cover 54 km + Time taken to cover 63 km = 3 h

∴ 54x+63x+6=3 ⇒ 54x+324+63xx(x+6)=3 ⇒ 117x+324=3(x2+6x) ⇒ 3x2-99x-324=0 ⇒ x2-33x-324=0 ⇒ x2-33x-108=0 ⇒ x2-36x+3x-108=0 ⇒ x(x-36)+3(x-36)=0 ⇒ (x-36)(x+3)=0 ⇒or x-36=0 or x+3=0 ⇒or x=36 or x=-3 ∴ x=36

(Speed cannot be negative)

Hence, the first speed of the train is 36 km/h.

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