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?

Open in App

Solution

Let the original average speed of train be x.
Time taken by train to cover 63 km with original speed =
Time taken by train to cover 72 km with increased speed = $fraction numerator 72 over denominator x plus 6 end fraction$

It is given that ;

$\frac{63}{x} + \frac{72}{x + 6} = 3$

$fraction numerator 63 left parenthesis x plus 6 right parenthesis plus 72 x over denominator x left parenthesis x plus 6 right parenthesis end fraction equals 3 fraction numerator 63 x plus 378 plus 72 x over denominator x squared plus 6 x end fraction equals 3 378 plus 135 x equals 3 x squared plus 18 x 3 x squared minus 117 x minus 378 equals 0 x squared minus 39 x minus 126 equals 0 x squared minus 42 x plus 3 x minus 126 equals 0 x left parenthesis x minus 42 right parenthesis plus 3 left parenthesis x minus 42 right parenthesis equals 0 left parenthesis x plus 3 right parenthesis left parenthesis x minus 42 right parenthesis equals 0 x equals 42 comma negative 3$
Speed cannot be negative, so the original average speed is 42km/hr.

Suggest Corrections

763

Similar questions

Q. A trains travels at a certain speed for a distance of

63 k m

& then travels a distance

72 k m

at an average speed of

6 k m / h

more than its original speed. If it takes

3 h

to complete the total journey then find its original avg 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 ?

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 per hour more than its original speed if it takes 3 hours to complete total journey what is the original speed ?

My solution :

63/x + 72/(x+6) = 3

After solving I got the answer => x=42

I wrote the answer as the train's original average speed is 42km/hr .

Is it correct ??????

Q. A bus travels at a certain average speed for a distance of

75 k m

and then travels a distance of

90 k m

at an average speed of

10 k m / h r

more than the first speed. If it takes

3

hours to complete the total journey. Find its original speed.

Join BYJU'S Learning Program

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?

Let the original average speed of train be x. Time taken by train to cover 63 km with original speed = Time taken by train to cover 72 km with increased speed = It is given that ; 63x+72x+6=3 Speed cannot be negative, so the original average speed is 42km/hr.