A car takes 2 hours more to cover a distance of 480 km when its speed is reduced by 8 km/hr. Find its usual speed.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 48 km/hr
The time at the reduced speed minus the time at the usual speed equals the extra 2 hours.
Let the usual speed be \(v\) km/hr
\(\displaystyle \frac{480}{v-8}-\frac{480}{v}=2\)
\(\displaystyle \frac{480\times8}{v(v-8)}=2\), so \(v(v-8)=1920\)
\(v^{2}-8v-1920=0\), that is \((v-48)(v+40)=0\)
Speed is positive, so \(v=48\) km/hr
Check: \(\displaystyle \frac{480}{40}-\frac{480}{48}=12-10=2\) hours