# 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?

#### 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.

Concept: Heights and Distances
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