Time, Speed, and Distance

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datonman: Senior | Next Rank: 100 Posts; Posts: 53; Joined: Wed May 28, 2014 9:36 pmFollowed by: 1 member

by datonman » Wed Feb 04, 2015 10:50 am

Hello,

Sultan walks at 14km/hr instead of 10km/hr, in which he would have walked 20km more. The actual distance traveled by him is what:

In this question the time is constant.

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Source: Beat The GMAT — Problem Solving | Wed Feb 04, 2015 10:50 am

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by Brent@GMATPrepNow » Wed Feb 04, 2015 11:11 am

datonman wrote:Hello,

Sultan walks at 14km/hr instead of 10km/hr, in which he would have walked 20km more. The actual distance traveled by him is what:

In this question the time is constant.

Sultan walks at 14km/hr instead of 10km/hr....
At this FASTER speed, Sultan walks an ADDITIONAL 4 km every hour [14km per hour - 10km per hour = 4km per hour]

....in which he would have walked 20km more
So, Sultan walked an ADDITIONAL 20 km

Time = distance/speed
= 20/4
= 5 hours

So, Sultan walked for a total of 5 hours.

The actual distance traveled by him is what?
Sultan walked at a speed of 14 km/hr
Sultan walked for 5 hours
Distance = (speed)(time)
= (14)(5)
= 70 km

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Brent

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Wed Feb 04, 2015 11:12 am

Hi, Datonman.

Do you mean that Sultan walked at 14km/hour for, say, T hours, and ended up going 20 km farther than he would have gone had he been walking at 10km/hour for that same T hours?

If so, the distance he'd cover walking at 14km/hour for T hours would be 14T. (R*T = D)

The distance he would have covered walking at 10km/hour for T hours would have been 10T.

We know that the distance he walked at 14 km/hour is 20 more than it would have been had he walked at 10km/hour. So we know that
14T = 10T + 20
4T = 20
T = 5.

If he walked for 5 hours, then he walked 14*5 = 70 km at 14km/hour and would have walked 10*5 = 50 at 10km/hour.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Feb 04, 2015 11:43 am

David brings up a good point. The question is somewhat ambiguous.

I assumed that, at 14kmh, that Sultan walked 20km FARTHER than he would have walked at 10kmh.
Is that the correct interpretation?
Or is that that the Sultan walked 10kmh and would have walked 20km FARTHER if he had walked at 14kmh?

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Thu Feb 05, 2015 10:26 am

datonman wrote:Hello,

Sultan walks at 14km/hr instead of 10km/hr, in which he would have walked 20km more. The actual distance traveled by him is what:

In this question the time is constant.

Considering the question as
"Sultan covers a distance that is 20 km more if he walks as 14Km/Hr instead of walking at 10 Km/Hr for the same time. Find the distance covered by Sultan when he walked at 10 Km/Hr.."

Distance = Speed x Time

for Constant TIME

D1 / S1 = D2 / S2

[Let, d is the distance covered at speed 10km/hr and (d+20) is the distance covered at 14 km/hr in same time]

d/10 = (d+20)/14
i.e. 14d = 10d + 200
i.e. 4d = 200
i.e. d = 50

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Mon Feb 09, 2015 12:01 am

If you assume the modifier is placed correctly and the verb tenses are correct -- a generous assumption, given the standards of grammar on display in the prompt -- then the question is something like:

"If Sultan had walked at 10km/hr, he would've walked 20 kilometers further than he did at 14km/hr. How far did he walk, in kilometers?"

The intent seems to be that he spent the same amount of TIME in each hypothetical trip, but would've walked further in the 10km/hr trip due to the slower speed.

This gives us two equations:

10km/trip
R = 10
T = t
D = 10t

14km/trip
R = 14
T = t
D = 14t

We're told that the first trip is 20km longer, so 10t = 14t + 20, which reduces to -4t = 20, or t = -5. So Sultan has wandered into a wormhole, traveled for -5 hours back in time, and saved himself a 20 kilometer slog. Good for him!

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