A person has to cover a distance of 120 km. If he increases his speed by 10 km/hr, he reaches 1 hour earlier. Find his initial speed (in km/hr).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 30
The time at the usual speed minus the time at the higher speed must equal the 1 hour saved.
Let the initial speed be \(v\) km/hr
\(\displaystyle \frac{120}{v}-\frac{120}{v+10}=1\)
\(\displaystyle \frac{120\times10}{v(v+10)}=1\), so \(v(v+10)=1200\)
\(v^{2}+10v-1200=0\), that is \((v+40)(v-30)=0\)
Speed is positive, so \(v=30\) km/hr
Check: \(\displaystyle \frac{120}{30}-\frac{120}{40}=4-3=1\) hour