A school bus transported an excursion party to a picnic spot 150 km away. While returning , it was raining and the bus had to reduce its speed by 5 km/h , and it took one hour longer to make the return trip. Find the time taken to return.

Let the speed of bus while reaching picnic spot be x km/h

Since, the speed of bus decrease by 5 km/h due to rain hence, speed of bus in rain = (x - 5) km/h

∴ Time taken to reach picnic spot = $\dfrac{150}{x}$ and Time taken to reach back to school = $\dfrac{150}{x - 5}$

According to given,

$\Rightarrow \dfrac{150}{x - 5} - \dfrac{150}{x} = 1 \\[1em] \Rightarrow \dfrac{150x - 150(x - 5)}{x(x - 5)} = 1 \\[1em] \Rightarrow \dfrac{150x - 150x + 750}{x^2 - 5x} = 1 \\[1em] \Rightarrow 750 = x^2 - 5x \text{ (On cross multiplying) } \\[1em] \Rightarrow x^2 - 5x - 750 = 0 \\[1em] \Rightarrow x^2 - 30x + 25x - 750 = 0 \\[1em] \Rightarrow x(x - 30) + 25(x - 30) = 0 \\[1em] \Rightarrow (x + 25)(x - 30) = 0 \\[1em] \Rightarrow x + 25 = 0 \text{ or } x - 30 = 0 \\[1em] x = -25 \text{ or } x = 30$

Since speed of bus cannot be negative hence, x ≠ -25.

∴ x = 30

If x = 30 , x - 5 = 25.

Time taken to return = $\dfrac{150}{x - 5}$ hours = 6 hours.

Hence, time taken on return trip is 6 hours.