Question

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 ?​

Answer 1

☆ Solution ☆

Given :-

• 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.

To Find :-

• What is the original average speed ?

Step-by-Step-Explaination :-

Let the original speed be x

As we know that :-

Distance = Speed × Time

Speed = Distance / Time

Time = Distance / Speed

We have,

Distance travels = 63 km

Next distance travelled = 72 km

Speed = ( x + 6 ) km/ h

Time = 72/ ( x + 6 ) hrs

63 / x + 72 / x + 6 = 3

Total journey completed in 3 hour.

According to the question,

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

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

=> 21 ( x + 6 ) + 24x = x ( x + 6 )

=> 45x + 21 × 6 = x^2 + 6x

=> x^2 - 39x - 126 = 0

=> x^2 - 42x + 3x - 126 = 0

=> x ( x - 42 ) + 3 ( x - 42 ) = 0

=> ( x - 42 ) ( x + 3 ) = 0

=> x = 42 and - 3

Hence,

42 km/hr is the original average speed.

Answer 2

$\bigstar \underline{\underline{\mathfrak{Given:-}}}$

• A train travels at a certain average speed for a distance of 63 km.
• And travels  Distance of 72 km at an average speed of 6 km/hr more than its original speed.
• Total time taken to complete journey = 3hours.

$\bigstar \underline{\underline{\mathfrak{To\ find:-}}}$

• The original average speed.

$\bigstar \underline{\underline{\mathfrak{Solution:-}}}$

We know:

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❥Time = Distance/speed

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Let the average original speed = 'x'

Then,

=>Time taken to cover 63km = 63 /x hrs.

=> Time taken to cover 72km at an avg speed of 6kmph more than original speed = 72/(x+6).

According to question:

Total time taken = 3hrs.

↬ Time taken to cover 63km + Time taken to cover 72km at an avg speed of 6kmph more than original speed = 3hours .

$:\implies \sf \frac{63}{x} + \frac{72}{x+6} =3\\\\:\implies \sf \frac{21}{x} +\frac{24}{x+6} =1\\\\:\implies \sf 21(x+6)+24(x)=(x)(x+6)\\\\:\implies \sf 21x+126+24x=x^2+6x\\\\:\implies \sf 45x+126=x^2+6x\\\\:\implies \sf x^2+6x-45x-126=0\\\\:\implies \sf x^2-39x-126=0\\\\:\implies \sf x^2-42x+3x-126=0\\\\:\implies \sf x(x-42)+3(x-42)=0 \\\\:\implies \sf (x+3)(x-42)=0\\\\:\implies \sf x+3=0 \ \ \ (or)\ \ \ x-42=0\\\\:\implies \underline{\boxed{\bold{x=-3,42}}}$

But speed cannot be negative,

Hence,  The original average speed = 42 km/h

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ღ More Shots :-

❥ Distance = speed×time

❥ Speed = distance / time

❥ Tricks to solve question regarding speed,distance,time:

• Speed, distance, and time problems ask to solve for one of the three variables given certain information.
• In these problems, objects are moving at either constant speeds or average speeds.  
• In Most problems  values for two variables will be given and they  ask for the third.
• Pay attention to the units for speed, distance, and time. Converting units may be required to get a correct answer.

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HOPE IT HELPS !