A fast train takes 3 hours less than a slow train for a journey of 600 km. If the speed of the fast train is 10 km/hr higher than that of slow train, then find the speed of the slow train.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 40 km/hr
Time \(=\) distance \(\div\) speed, and the fast train’s time is 3 hours less than the slow train’s for the same 600 km. Let the slow train’s speed be \(v\) km/hr; the fast train’s is then \(v+10\).
Slow train’s time minus fast train’s time is 3 h: \(\displaystyle \frac{600}{v}-\frac{600}{v+10}=3\)
The left side over one denominator is \(\displaystyle \frac{6000}{v(v+10)}\), so \(v(v+10)=2000\)
This is the quadratic \(v^{2}+10v-2000=0\), which factorises as \((v+50)(v-40)=0\)
A speed cannot be negative, so \(v=\) 40 km/hr
Shortcut:
Try the options: at 40 km/hr the slow train takes \(600\div40=15\) h and the fast train, at 50 km/hr, takes \(600\div50=12\) h
The difference is 3 h, as the question says