Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

SDT # 1

A person travels equal distances with speeds of 3 km/hour, 4 km/hour and 5 km/hour and takes a total time of 47 minutes. What is the total distance travelled?

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

SDT # 2

Two trains are running at 40 km/hour and 20 km/hour respectively in the same direction. The faster train completely passes a man in the slower train in 5 seconds. What is the length of the faster train?

Character is who you are when no one is looking.

Offline

**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

SDT1

Offline

**ryos****Member**- Registered: 2005-08-04
- Posts: 394

El que pega primero pega dos veces.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

Well done, ryos!

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

SDT # 3

An express train traveling at 72 km/hr speed crosses a goods carriage train traveling at 45 km/hr speed in the opposite direction in half a minute. Alternatively, if the express train were to overtake the goods carriage train, how long will it take to accomplish the task? Assume that the trains continue to travel at the same respective speeds as mentioned in the earlier case.

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

SDT # 4

X is picked up by his father by car from school everyday and they reach home at 5.00 p.m. One day, since the school got over an hour earlier than usual, he started walking towards home at 3 km/hr. He met his father on the way and they reached home 15 minutes earlier than their usual time. What is the speed of the car?

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

SDT # 5

An hour after Allan started from his college towards Cindy's home,

a distance of 53 km, Cindy started from her home on the same

road towards Allan's college. If Allan's speed was 4 km per hour and Cindy's was 3 km per hour, how many kilometres from Cindy's home did the two meet?

Character is who you are when no one is looking.

Offline

**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

SDT #3

Assumption: The definition of "passing" means from the moment the front of the train starts to pass until the moment that the end of the train finishes passing.

The trains initially are heading toward each other. Therefore, their combined speed is 72 + 45 = 117kph

It takes 30 seconds for them to pass, so the combined length of the trains is 117/120 km

When travelling in the same direction, the differential speed is only 27kph.

In order to travel 117/120km at 27kph, it will take:

(117/120) * (60/27) minutes = 2.1666 minutes = 2 minutes 10 secs

Offline

**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

SDT #4

I like this one! Some good red herrings. Started off thinking about what time dad left home; what is the distance from school to home? did dad always manage to arrive exactly on time? why did he call his son "X"? Actually, none of it is relevant (but I do feel sorry for the poor boy branded with such a name)

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

SDT # 3 is correct! Well done, ashwil! I don't remember the answer to the next problem, nor do I have the time to check your solution now. I shall try SDT#4 later before telling whether you are right or wrong! **Well done, ashwil**

Character is who you are when no one is looking.

Offline

**ashwil****Member**- Registered: 2006-02-27
- Posts: 121

SDT #5

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

**Excellent, ashwil, both the answers (SDT#3 and SDT#5) are correct! Keep up the good work! **

Character is who you are when no one is looking.

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

SDT # 6

A man riding a cycle at 12 km/hour can reach his village in 4½ hours. If he is delayed by 1½hour at the start, in order to reach his destination in time, at what speed should he ride?

Character is who you are when no one is looking.

Offline

**Dionysus****Member**- Registered: 2006-03-06
- Posts: 9

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

Character is who you are when no one is looking.

Offline

**vgopalak****Member**- Registered: 2006-04-05
- Posts: 3

ganesh wrote:

SDT # 4

X is picked up by his father by car from school everyday and they reach home at 5.00 p.m. One day, since the school got over an hour earlier than usual, he started walking towards home at 3 km/hr. He met his father on the way and they reached home 15 minutes earlier than their usual time. What is the speed of the car?

[Solution]

H=Home, S=School, M=Father and Son meet

H========================================M=============S

(Time = ?) (Car arrives at 5.00 pm)

The car arrives at 5.00 pm at point 'S'. But since Mr X started walking at

4.00 pm, they will meet at a point 'M'.

The car saved travel distance M -> S and S -> M. This resulted in 15 minutes

savings. Assuming uniform speed, it takes 7 1/2 minutes from 'M' to 'S' and

vice-versa. So both meet at 4:52 1/2 pm. The Son had been walking from 4.00 pm

till this time, which is 52 1/2 min.

The same distance is covered by the car in just 7 1/2 min. Therefore the car

travels at 52.5/7.5 times the walking speed of Mr X (3 km/hr).

********************************************************

Speed of the car = 3 X 52.5/7.5 = 21 km/hr

Distance from S = 21 X 7.5/60 = 2 5/8 km (2.625 km)

*******************************************************

Offline

**vgopalak****Member**- Registered: 2006-04-05
- Posts: 3

ganesh wrote:

SDT # 6

A man riding a cycle at 12 km/hour can reach his village in 4½ hours. If he is delayed by 1½hour at the start, in order to reach his destination in time, at what speed should he ride?

[Solution]

Total distance = 12 X 4.5 = 54 Kms

If he starts 1.5 hrs late, then he has only (4.5 - 1.5) = 3 Hrs to commute 54 Kms.

So he has to cycle at speed of :

**V = 54/3 = 18 Km/hour**

Offline

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,403

**Excellent, vgopalak! Keep it up! **

Character is who you are when no one is looking.

Offline

**Sudeep****Member**- Registered: 2008-07-21
- Posts: 20

A thief escaped from police custody. His speed is 40 km/hr. The police realized it after 3 hr and started chasing him in the same direction at 50km/hr. The police had a dog which could run at 60 km/hr. The dog would run to the thief and return to the police and then would turn back towards the thief and so on until the thief is caught. Find the total distance travelled by the dog in the direction of the thief.

Offline

**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

In 3 hrs the thief has run 120 km. Relative speed of thief and police is 10 kmph. So, police will take 12 hrs to catch the thief and thus the dog will run for the same amount of time (no matter in what direction!)!

Hence, the total distance travelled by the dog is 12*60=720 km!

If two or more thoughts intersect with each other, then there has to be a point.

Offline

**Sudeep****Member**- Registered: 2008-07-21
- Posts: 20

ZHero wrote:

In 3 hrs the thief has run 120 km. Relative speed of thief and police is 10 kmph. So, police will take 12 hrs to catch the thief and thus the dog will run for the same amount of time (no matter in what direction!)!

Hence, the total distance travelled by the dog is 12*60=720 km!

720 is the total distance covered by dog, the question asks the distance covered by dog in direction of the thief... you have to remove the distance which dog covered coming back to police each time after seeing the thief...

Offline

**ZHero****Real Member**- Registered: 2008-06-08
- Posts: 1,889

Aah! Got it!

When running towards the thief, the relative speed of dog is 60-40=20 kmph and when running back towards the police, the relative speed is 60+50=110 kmph!

Now, the total distance travelled by dog i.e. 720 km is travelled with two speeds of 20 kmph and 110 kmph in 12 hrs! Let x be the time for which he runs in the thieves direction!

Hence, 110(12-x)+20x=720

x=20/3

Therefore, distance travelled in the direction of thief is 60*20/3=400 km !!

If two or more thoughts intersect with each other, then there has to be a point.

Offline

**Sudeep****Member**- Registered: 2008-07-21
- Posts: 20

Rohan fires two bullets from the same place at an interval of 12 minutes but Raju sitting in a train approaching the place hears the second report 11 minutes 30 seconds after the first. What is the approximate speed of train (if sound travels at the speed of 330 meters per seconds)?

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,522

hi ganesh

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

Offline

Pages: **1**