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A bus travels at a certain average speed for a distance of 75 km and then travels a distance of 90 km at an average speed of 10 km/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed? - Mathematics

A bus travels at a certain average speed for a distance of 75 km and then travels a distance of 90 km at an average speed of 10 km/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed?

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Solution

Let x be the initial speed of the bus.

We know that 

`"Distance"/"Speed"="time"`

Thus,we have,

`75/x+90/(x+10)=3 hours`

`(75(x+10)+90x)/(x(x+10))=3`

`75 (x+10)+ 90x= 3x(x+10)`

`75x+750+90x=3x^2+30x`

`3x^2-165x-750+30x=0`

`3x^2-135x-750=0`

`x^2-45x-250=0`

`x^2-50x+5x-250=0`

`x(x-50)+5(x-50)=0`

`(x+5)(x-50)=0`

`(x+5)=0 or (x-50)=0`

`x=-5 or x=50`

Speed cannot be negative and hence first speed of the train is 50 km/hour.

  Is there an error in this question or solution?
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