Question : Travelling a distance of 1000 km, a train slowed down due to repairs to the tracks. Its average speed for the trip was reduced by 75 km/hr and the time of travel increased by 3 hours. The original duration of the travel is:
Option 1: 6 hours
Option 2: 5 hours
Option 3: 5.5 hours
Option 4: 6.5 hours
Correct Answer: 5 hours
Solution :
Distance, $d = 1000$ km
Let $s$ be the average speed and $t$ be the time taken.
$d = s × t$
⇒ $s = \frac{1000}{t}$ ----------(i)
⇒ $d = (s-75)(t+3)$
⇒ $st = st -75t +3s-225$
⇒ $75t+225 = 3s$
⇒ $75t+225 = 3×\frac{1000}{t}$
⇒ $t+3 = \frac{40}{t}$
⇒ $t^2+3t-40=0$
⇒ $t^2+8t-5t-40=0$
⇒ $t(t+8)-5(t+8)=0$
⇒ $(t-5)(t+8)=0$
$\therefore t=5$
Hence, the correct answer is 5 hours.
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