School-Safe Puzzle Games

## Speed and Distance Puzzle, Track Race

A man and his dog are racing on a circular track at constant speed. John can run once around the track in six minutes, and Ben (his Dog)  in four minutes. In how many minutes will Ben overtake John?

### 18 Comments to “Speed and Distance Puzzle, Track Race”

1. o.najaee | Profile

2.4 min
funny

2. Shawn | PUZZLE GRANDMASTER | Profile

12 minutes

3. suineg | PUZZLE MASTER | Profile

Ok, I think it can be solved this way: (hope that there is circular velocity here)
Assuming that both of them start at the same point and at the same moment, the dog overtake him, in time 0….01 cause he passed him, the dog velocity is greater than the man velocity, but I asumme that this mean when the dog meet again with his master.. so:
In an easy way:
John covers 1/3 of the lap distance in 2 minutes
Ben covers 1/2 of the lap distance in 2 minutes
1/2-1/3= 1/6 (distance that Ben gains over John every 2 min)
six time this time… Ben would have gained exactly 1 lap
that happen 6X2= 12 min… Ben meets John in 12 min so:
Ben would overtake John in 12 min and 1 nanosecond… jajaja, cool

4. Bobo The Bear | PUZZLE MASTER | Profile

(Assuming they both start at the same point on the track …

After 12 minutes, John will have done 2 laps, and his dog will have done 3 laps and will then overtake him.

5. Bobo The Bear | PUZZLE MASTER | Profile

One question: If John is running around the track, and the puzzle title says that it’s a bike race, does that mean that his dog is the one on the bicycle??

6. RK | Founder | Profile

Oops! title changed Bobo

7. Hex | PUZZLE MASTER | Profile

In 12 minutes, John would have made 2 laps and Ben 3.

8. munna | Profile

Assuming they John and Ben start from same point, Ben will overtake John in 12 minutes.

9. Falwan | Profile

x = time in hrs.

D = diameter

(xD/4) – (xD/6) = D

(x/4) – (x/6) = 1

3x – 2x = 12

x = 12

Mr. Ben will overtake Mr. John after 12 hrs.

10. Falwan | Profile

I considered the time in hours.

So 12 min. in that case.

11. RK | Founder | Profile

Very good, 12 min is correct

12. Hendy | Profile

J = 1/6 rpm (1 revolution/ 6 minutes)
B = 1/4 rpm (1 revolution/ 4 minutes)

rJ = t * 1/6 rpm
rB = t * 1/4 rpm

rJ = x min * 1/6 r/min
rB = x min * 1/4 r/min

rJ = x * 1/6 r = x * 1/6 r
rB = x* 1/4 r = x * 1/4 r

rB = rJ + 1
x * 1/4 r = x * 1/6 r + 1 r
1/4-1/6 = 1/12
1 r = x * 1/12 r
1 = x * 1/12
x = 12

12 * 1/6 = 2
12 * 1/4 = 3

Overtaken in 12 laps (revolutions).

13. Hendy | Profile

Oops! That should be time in minutes, not revolutions. Not paying attention!

14. Hedaiet El-Sabbahy | Profile

*Assume that the speed of the man is (Sm = 1/6 RPM)and speed of Dog is (Sd=1/4 RPM)
*Assume that they will meet again after (X) mins.
* Then the No. of rounds covered by Man = 1/6 X, and by the Dog = 1/4 X.
* As they will meet again, Then: (1/4 X = 1/6 X + 1).
* Then: (1/4-1/6) X = 1 ==> (1/12) X = 1 ==> X = 12 Mins.
THANKS FOR ALL

15. Tsopi | Profile

we must find at witch time man will have done x laps and dog x+1 laps
H 1 lap – 6 minutes/D 1 lap – 4 minutes
H 2 lap – 12 minutes/D 2 lap – 8 minutes
H 3 lap – 18 minutes/D 3 lap – 12 minutes

As we see at the time of 12 minutes the Human (H) has done 2 laps(x = 2) and the Dog(D) has made 3 (x + 1 = 2 + 1 = 3).

16. venkatg70 | Profile

Let a,b be the time taken by the person and dog respectively.

Let a>b
Let x be the time when they meet
Then,

x/a = fraction of the circular track covered by person
x/b = fraction of the circular track covered by dog

As they both run, gap created between them. When the gap (fraction of the track length)
approaches “n” where n = 1,2,3…, they meet.

For initial meet n =1, so

So x/b – x/a = 1

Solving, we get x = ab/(a-b)

For eg: when a=6 min, b=4 min, x = 12 min

17. swejhammer | Profile

12 minutes?? That answer doesn’t make any sense.
If the dog runs a lap in 4 minutes it is going to overtake the man before the man can finish his lap (in 6 min). The puzzle doesn’t say when they start, so we assume they start together. If so,the dog will immediately pull ahead and be ahead the entire race.

18. swejhammer | Profile

Oh, I see now… I thought you were all daft
Turns out the puzzle is just worded strangely. What you call “overtake” I would call “lap”.

When would the dog lap the man? Assuming they start together, the dog immediately overtakes the man and is in the lead. At 6 minutes when the man is finishing his first lap, the dog is already 1/2 around his second lap. At 12 the man has completed 2 laps and the dog is finishing his 3rd. The dog laps the man when he overtakes him for the second time.