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प्रश्न
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?
उत्तर
Let the first speed of the train be x km/h
Time taken to cover 54km`=54/x h` `(Time=(Distance)/(Speed))`
New speed of the train =`(x+6)`km/h
∴ Time taken to cover 63km=`63/(x+6) h`
According to the given condition,
Time taken to cover 54 km + Time taken to cover 63 km = 3 h
∴ `54/x+63/(x+6)=3`
⇒`(54x+324+63x)/(x(x+6))=3`
⇒` 117x+324=3(x^2+6x)`
⇒`3x^2-99x-324=0`
⇒`x^2-33x-324=0`
⇒`x^2-33x-108=0`
⇒`x^2-36x+3x-108=0`
⇒`x(x-36)+3(x-36)=0`
⇒`(x-36)(x+3)=0`
⇒`x-36=0 or x+3=0`
⇒`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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