#### Question

Some school children went on an excursion by bus to a picnic spot at a distance of 300 km. While returning, it was raining and the bus had to reduce its speed by 5 km/hr and it took two hours longer for returning. Find the time taken to return.

#### Solution

Distance = 300 km

Let the original speed of the bud be x km/hr

While returning speed of the bus = (x - 5) km/ hr

From the given information we have

`300/(x - 5) - 300/x = 2`

`(300x - 300x + 1500)/(x(x - 5)) = 2`

`750/(x(x - 5)) = 1`

`x^2 - 5x - 750 = 0`

`x^2 - 30x + 25x - 750 = 0`

x(x - 30) + 25(x - 30) = 0

(x - 30)(x + 25) = 0

x = 30, -25

Since speed cannot be negative So x= 30

Speed of the bus while returining = 25 km/hr

Time taken by the bus to return = 300/25 hrs = 12 hrs

Is there an error in this question or solution?

Solution Some School Children Went on an Excursion by a Bus to a Picnic Spot at a Distance of 300 Km. While Returning, It Was Raining and the Bus Had to Reduce Its Speed by 5 Km/Hr and Concept: Quadratic Equations.