Question : A car left 4 hours later than the scheduled time but in order to reach its destination 480 km away in time, it had to increase its usual speed by 10 km/hr. What is the usual speed of the car?
Option 1: 40 km/hr
Option 2: 60 km/hr
Option 3: 30 km/hr
Option 4: 50 km/hr
Correct Answer: 30 km/hr
Solution :
Let the usual speed of the car as $v$ in km/hr.
The time it takes to travel 480 km at the usual speed is $\frac{480}{v}$ hours.
Because the car left 4 hours later than scheduled, it had to travel at a speed of $(v + 10)$ km/hr to reach its destination on time.
The time it takes to travel 480 km at this increased speed is $\frac{480}{(v + 10)}$ hours.
$⇒\frac{480}{v}=\frac{480}{(v + 10)}+4$
$⇒v^2+10v-1200=0$
$⇒(v+40)(v-30)=0$
So, $v=30$, as speed cannot be negative.
Hence, the correct answer is 30 km/hr.
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