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
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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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