Bunuel
Two persons A and B run at constant speeds of a miles per hour and b miles per hour respectively. They start running toward each other at the same time from a distance of d miles. How much time will they take to meet?
(1) If A and B ran at speeds of a/2 and 2b respectively, they would take the same amount of time to meet.
(2) If they both ran at 1 mile per hour slower, they would take double the time to meet.
(1) If A and B ran at speeds of a/2 and 2b respectively, they would take the same amount of time to meet. Lets say they take \(t\) hours to meet. Then:
\(\frac{a}{2}.t+ 2b.t =d \)
INSUFF.(2) If they both ran at 1 mile per hour slower, they would take double the time to meet. Lets say A meets at distance \(p\) when travelling at the original speed. Hence time taken to meet by A \(= \frac{p}{a}\)
Now when speed is \(1\) mile per hour slower, time taken to meet is doubled so: \(\frac{p}{a-1} = 2* \frac{p}{a}\), \( \right \) \( a=2 \)
Similarly \(b=2 \)
However we still do not know \(d.\)
INSUFF.1+2
We still do not know \(d.\)
Time taken to meet will change based on distance.
INSUFF.Ans E
Extra : using (ii) we know \(a=b =2\) and using (i) we know they take the same time to meet, when speed is \(1\) and \(4\) respectively.
Let's say they meet in \(1\) hr then \(1*1 + 4*1 = 5 \)
Let's say they meet in \(2\) hrs then \(1*2 + 4*2 = 10\)
Thus we see time taken to meet changes with distance.
Hope it helped.