Question

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/hr, and it took one hour longer to make the return trip. Find the time taken to return.

Answer 1

Distance = 150km
Let the speed of bus = x km/hr

∴ Time taken = `(150)/x"hour"`

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

∴ Time taken = `(150)/(x - 5)`
According to the condition

`(150)/(x - 5) - (150)/x` = 1

⇒ `150((1)/(x - 5) - (1)/x)` = 1

⇒ `150((x - x + 5)/(x(x - 5)))` = 1

⇒ `(1500 xx 5)/(x^2 - 5x)` = 1

⇒ x² - 5x = 750
⇒ x² - 5x - 750 = 0
⇒ x² - 30x + 25x - 750 = 0
⇒ x(x - 30) + 25(x - 30) = 0
⇒ (x - 30)(x + 25) = 0
Either x - 30 = 0,
then x = 30
or
x + 25 = 0,
then x = -25,
but it is bot possible as it is negative.
∴ Speed of bus = 30km and time taken while returning

= `(150)/(x - 5)`

= `(150)/(30 - 5)`

= `(150)/(25)`
= 6hours.