Question

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 it took two hours longer for returning. Find the time taken to return.

Answer 1

Distance = 300 km

Let the original speed of the bus 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`

x² – 5x – 750 = 0

x² – 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 returning = 25 km/hr.

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