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

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Solution

We know the speed,distance,time $t i m e = \frac{d i s t a n c e}{s p e e d}$
Let the speed be $v k m / h r$ and the time taken is $t h r$ for the journey to the picnic such that $300 = v (t)$ . Using the given information
$300 = (v - 5) (t + 2) = (v - 5) (\frac{300}{v} + 2)$
$300 (\frac{5}{v}) = 2 (v - 5) ⟹ v^{2} - 5 v - 750 = 0 ⟹ v = \frac{5 \pm 55}{2}$
$v = 30 k m / h r ⟹ t = 10 h r$
time taken for return journey is $12 h r$ .

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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.

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