Speed/Distance

Expert replies

MI3: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Sat Feb 26, 2011 11:22 amFollowed by: 1 member; Thanked: 1 times

by MI3 » Tue May 31, 2011 5:49 am

Q. A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continue to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?

Whilst I don't have a list of answers with the question, I got 20 mins as the answer. Can the experts out there opine?

Thanks,
M.

Source: Beat The GMAT — Problem Solving | Tue May 31, 2011 5:49 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Tue May 31, 2011 6:04 am

Hi,
The relative speed is 20-4 = 16mph.
So, 5 mins after the cyclist passed hiker, distance between them will be 16(1/12) = 4/3 miles
So, the hiker will take (4/3)/4 = 1/3 hour to meet cyclist. i.e., 20 mins

Cheers!

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Tue May 31, 2011 6:04 am

In 5 minutes, cyclist covers a distance of 20*5/60 = 5/3 miles.
Hiker covers 4*5/60 = 1/3 miles.
thus hiker has to cover 5/3-1/3 = 4/3 extra miles to catch up with the cyclist.
distance = 4/3 miles, speed = 4miles/hr,
thus time = (4/3)/4 hr = 1/3hr = 20 minutes.
IMO 20 minutes

romanov: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Mon May 23, 2011 2:01 amFollowed by: 4 members; Thanked: 2 times

by romanov » Tue May 31, 2011 6:07 am

hey i think 20 mins is correct....heres how i solved it.

Speed of hiker = 4 miles/hr
Speed of cyclist = 20 miles/hr
Therefore,
Since they are travelling in the same direction
Relative speed of cyclist wrt hiker = 20-4= 16 miles/hr

Now,
The distance travelled by cyclist wrt hiker in 5 mins = 16 * 5/60 miles

Therefore
Time taken by the hiker to cover this distance = 16 * 5/60 * 1/4 hours = 1/3 hours = 20 mins

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