Problem Solving

ques

A police officer, travelling at 100 miles per hour, pursues philip who has 30 minutes head start. The police officer overtakes philip in two hours. Find Philip's speed?

alltimeacheiver wrote:ques

A police officer, traveling at 100 miles per hour, pursues Philip who has 30 minutes head start. The police officer overtakes Philip in two hours. Find Philip's speed?

Let Philip's speed = X miles per hour
In half an hour , he has traveled = X mph *0.5 hr = X/2 miles
Police officer is covering the same distance in 2 hours
Relative speed of Police officer = 100 - X
Hence , distance traveled => (100 - X)*2 = X/2
On solving further = > 400 = 5X
X = 80
Philip's speed ( S) = 80 miles per hour

alltimeacheiver wrote:ques

A police officer, travelling at 100 miles per hour, pursues philip who has 30 minutes head start. The police officer overtakes philip in two hours. Find Philip's speed?

Let the speed of philip be v miles per hour.
so distance covered by philip in 2 hrs and 30 min = vx2.5 = 2.5v miles
distance covered by police officer in 2 hrs = 100x2 = 200 miles
so 2.5 v = 200 --> v = 200/2.5 = 80 miles per hour.

Dear alltimeacheiver, please post a PS with its 5 answer choices as always expected, so that more than very a few approaches could also be discussed for the same good question. Conceptually, this question is absolutely not out of GMAT, but the wordings like 30 minutes head start or Find Philip's speed? show that the source is not genuinely GMATish.

Great work 6983manish!

If We figure out that both travel the same distance = 200 miles then I think this can be done without using paper & pen.

Philip takes 5/4 of the time poilce officer takes . So it must be traveling at a speed 4/5 of the police officer.

So (4/5) * 100 = 80 . Done.