A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

Answer

36 km/hr

Explanation

Let the first speed be x km/hr. Then,
`(54)/(x)+(63)/((x+6))=3implies9[(6)/(x)+(7)/((x+6))]=3`
`implies3[6(x+6)+7x]=x(x+6)impliesx(x+6)implies3(13x+36)`
`impliesx^(2)-33x-108=0.`