Vincen wrote: ↑

Thu Jun 24, 2021 10:19 am

While driving on a highway, Harry and Ron crossed checkpoint \(P\) at \(9\) am and \(10\) am, at individual speeds of \(30\) mph and \(40\) mph respectively. Professor Snape started cycling in the same direction as Harry and Ron, from point \(Q\) at \(8\) am at \(15\) mph. If Harry and Ron met each other at \(Q,\) then at what distance from \(Q\) Ron met Professor?

A. 40
B. 60
C. 80
D. 120
E. 160

Answer: D

Source: e-GMAT

Harry and Ron both met at point \(Q,\) means that they travelled the same distance, \(D.\)
Harry D = Speed x (time + 1) ..... since harry took 1 hour more than Ron to cover same distance
Ron D = Speed x Time

Equating both distances, \(30t+30 = 40t\)
So, \(t = 3\) hours.

Ron took off \(2\) hours after Snape and reached at \(Q,\) therefore, Ron took \(5\) hours to reach \(Q\)
therefore, in 5 hours, snape covered \(5 \times 15 = 75\) miles.

Use relative speed for finding relative time
So, Ron require relative time \(T\) to cover these \(75\) miles, i.e. \(\dfrac{75}{40-15} \ldots\) since both travelling in same direction

\(T = 3\) hours.
In these \(3\) hours, Ron would have covered, \(3 \times 40 = 120\) miles.

Hence, Ron met Snape at \(120\) miles.