Tricky Speed/Distance question..

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mav800rick: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Sun Apr 27, 2008 4:22 pm

by mav800rick » Mon Jun 02, 2008 4:22 pm

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?

-Answer and approach please.

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Source: Beat The GMAT — Problem Solving | Mon Jun 02, 2008 4:22 pm

sasi78: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Fri Apr 04, 2008 11:28 pm

by sasi78 » Mon Jun 02, 2008 7:02 pm

Distance covered by cyclist in 5 mins = (20/60)*5 = 5/3 miles
Time taken for the hiker to cover 5/3 miles = (5/3)/(4/60) = 25 mins.

So, the answer is 25 mins.

Can someone confirm this pl.

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mandy12: Junior | Next Rank: 30 Posts; Posts: 24; Joined: Mon Mar 31, 2008 4:11 am

by mandy12 » Mon Jun 02, 2008 7:39 pm

Distance covered by cyclist in 5 mins = (20/60)*5 = 5/3 miles
Distance covered by hiker in 5 mins = (4/60)*5 = 1/3 miles

So the difference when cyclist stops is 4/3 miles

Time taken for the hiker to cover 4/3 miles = (4/3)/(4/60) = 20 mins.

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chidcguy: Master | Next Rank: 500 Posts; Posts: 438; Joined: Mon Feb 12, 2007 9:44 am; Thanked: 26 times

by chidcguy » Mon Jun 02, 2008 7:45 pm

I arrived at the same solution of 20 min as did mandy12, using the same approach

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netigen: Legendary Member; Posts: 631; Joined: Mon Feb 18, 2008 11:57 pmFollowed by: 3 members; Thanked: 29 times

by netigen » Mon Jun 02, 2008 10:21 pm

first find the difference in the speed = 20-4 =16

so in 5 min the distance between them will be = 16 x 5/60

the hiker will cover this distance in 16 x 5/60 x 1/4 hrs = 1/3 hr = 20 mins

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MBALA2009: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Wed May 07, 2008 12:08 pm; Location: Toronto, Canada

by MBALA2009 » Thu Aug 07, 2008 8:10 pm

netigen wrote:first find the difference in the speed = 20-4 =16

so in 5 min the distance between them will be = 16 x 5/60

the hiker will cover this distance in 16 x 5/60 x 1/4 hrs = 1/3 hr = 20 mins

Quick question - Where does the 1/4 come from in the last equation?

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Thu Aug 07, 2008 8:26 pm

MBALA2009 wrote:
netigen wrote:first find the difference in the speed = 20-4 =16

so in 5 min the distance between them will be = 16 x 5/60

the hiker will cover this distance in 16 x 5/60 x 1/4 hrs = 1/3 hr = 20 mins
Quick question - Where does the 1/4 come from in the last equation?

Short answer- it's the reciprocal of the hiker's speed. Longer answer:

From the time/distance/speed equation, we have s = d/t, which we can rewrite:

t = d/s

In netigen's solution, he found the distance to be 16 x 5/60 miles. The hiker's speed was 4 miles per hour, so

t = d/s = (16 x 5/60)/4, or equivalently
t = d/s = (16 x 5/60)(1/4)

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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