Time,Speed & Distance

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Wed Sep 14, 2011 6:26 am

A leaves home at 9: 30 a.m. daily to reach his office at 10:30 a.m. He travels by his bike at a speed of 36 kmph. One a particular day, he left home at the usual time but his bike broke down after travelling some distance. After waiting for 15 minutes he walked to the office at a speed of 18 kmph and reached the office at 11 a.m. Find the distance for which A had to walk?

A)27
B) 9
C)18
D) 22.5
E) None of these

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Source: Beat The GMAT — Problem Solving | Wed Sep 14, 2011 6:26 am

gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Wed Sep 14, 2011 7:54 am

Since he normally goes for 1 hour at 36 km/hr, the total distance to work is 36.

Let x = distance biked before stopping.

Time spent biking = Distance/Rate = x/36
Time spent waiting = 1/4 ALWAYS USE HOURS
Time spent walking = Distance/Rate = (36-x)/18
Total time = 3/2 hours

x/36 + 1/4 + (36-x)/18 = 3/2
Multiply everything on both sides by 36
x + 9 + (72-2x) = 54
[spoiler]81 - x = 54
x = 27[/spoiler]

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Wed Sep 14, 2011 9:57 am

distance walked 9, b

Success doesn't come overnight!

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Wed Sep 14, 2011 10:58 am

Distance from home to office

D = 36*1 = 36km

On the day the bike broke down, let's say he travelled a distance of x km at 36km/hr for some time t

x=36*t

He covers the rest of the distance (36-x) at 18km/hr for (3/2-t)hrs. As he takes 30 minutes more

36-x = 18*(3/2-t)
36-36t = 27-18t
t=1/2hr
x=18. Therefore distance he walked is 36-18 = 18

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robosc9: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Dec 23, 2010 3:38 pm

by robosc9 » Thu Sep 15, 2011 7:44 pm

shankar.ashwin wrote:A leaves home at 9: 30 a.m. daily to reach his office at 10:30 a.m. He travels by his bike at a speed of 36 kmph. One a particular day, he left home at the usual time but his bike broke down after travelling some distance. After waiting for 15 minutes he walked to the office at a speed of 18 kmph and reached the office at 11 a.m. Find the distance for which A had to walk?

A)27
B) 9
C)18
D) 22.5
E) None of these

IMO B. Distance walked is 9 Kms

Time = 1 hr (10:30 - 9:30)
Speed = 36 Km/Hr (given, the speed with bike)

Therefore, total distance = 36 Kms

Now, he drives the bike for some distance. Let the time on bike = T1
Therefore, his distance traveled on bike = Speed x Time = 36 x T1

He walks the remaining distance.
Let's assume that the time to complete the walk = T2
Therefore, distance he walked = Speed x Time = 18 x T2

Total time he took when his bike broke was 1:30 Hrs (given 10:30am - 9am)
He waits for 15 mins

Therefore, the net time for bike ride (T1) + time for walking (T2) = 1:30 Hrs - 15 mins = 1Hr 15 mins = 5/4 Hrs

So, we know the total distance is 36 km

and

putting all the values together, we get

Total distance = 36T1 + 18T2 = 36

and we know

T1 + T2 = 5/4

Solving the equations, we would get T2 = 1/2 and therefore,

distance walked = 1/2 * 18 = [spoiler]9 Kms = answer choice B[/spoiler]

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Sep 16, 2011 3:02 am

shankar.ashwin wrote:A leaves home at 9: 30 a.m. daily to reach his office at 10:30 a.m. He travels by his bike at a speed of 36 kmph. One a particular day, he left home at the usual time but his bike broke down after travelling some distance. After waiting for 15 minutes he walked to the office at a speed of 18 kmph and reached the office at 11 a.m. Find the distance for which A had to walk?

A)27
B) 9
C)18
D) 22.5
E) None of these

We can plug in the answers, which represent the distance walked.
Since his biking speed is 36kph and the trip normally takes 1 hour, the total distance = 36k.
Since 1/4 of an hour is spent waiting, and the entire trip takes 1.5 hours, the total time spent walking and biking must be 1.25 hours.

Answer choice C: 18k walked at 18kph, 18k biked at 36kph
Time walking + time biking = 18/18 + 18/36 = 3/2.
Too long.
Less time must be spent walking.

Answer choice B: 9k walked at 18kph, 27k biked at 36kph
Time walking + time biking = 9/18 + 27/36 = 5/4.
Success!

The correct answer is B.

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