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Question
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?
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.
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