discussion topic: Time Speed Distance Puzzle

I found this interesting puzzle on net.

On a foggy night, a passenger car and a truck meet on a bridge that is so narrow that the two vehicles can neither neither pass nor turn. The car has proceeded twice as far onto the bridge as the truck, but the truck has required twice as much time as the car to reach this point. Each vehicle has only half its forward speed when in reverse. Which of the two vehicles should back up to allow both of them to cross the bridge in the minimum time?

This could be done a bit faster I guess.....

Let the time taken by car to travel the distance mentioned be 2 hrs.

Given that the truck has traveled half this distance in 4 hrs.

So, now if the car backs up, it will take 4 hrs to go back and the same distance will be covered by the truck in 8 hrs which means the car will go back first and has to wait for 4 more hrs for the truck to clear the bridge. After this the car will clear the bridge in 3 hrs. So time taken here = 8 + 3 = 11 hrs

I think we can quickly eliminate the case of truck back up here

If the truck backs up..forget the time taken for this.....in order to clear the entire bridge the truck will alone take 12 hrs which is more than the time taken in the previous case.

Hence, the car must back up.

hello sir
my name is raj
i have a doubt in time and distance topic
the problem is

"hero and hercules start simultaneously from P towards the same destination Q.when the distance between hero and hercules was 30 KM champ starts towards Q .the distance travelled by champ to overtake hercules is twice the distance travelled to overtake hero.the ratio of speeds of hercules and hero is 3:2.


1. what is the ratio of the speed of champ to hero?
a.4:1
b.3:1
c.2:1
d.none of these

2. what is the distance between hero and hercules when champ was equidistant from hero and hercules?

a.45KM
b.48KM
c.51.42KM
d.54.57KM

These two can be answered a bit fast if you can understand the following reasoning....

It is evident that by the time Champ started Hero has covered 60 km and Hercules has covered 90 km.

From the given question we can conclude that if d km is the distance covered by Champ to meet Hero, from the point where he met Hero he should travel another d km to meet Hercules.

Now since Champ meets Hero after traveling a distance of d km, it is implied that Champ traveled 60 km more than Hero. Now since he traveled another d km to meet Hercules, it is implied that by the time Champ meets Hercules, Hero is 60 km behind them.

So by the time Champ meets Hercules, the distance between Hero and Hercules is 60 km. Since the speed ratio of Hero and Hercules is 3 : 2, by the time Champ met Hercules, Hero covered 120 km out of which 60 km was covered earlier.

Hence, by the time Hero covers 60 km, Champ covered 180 km and hence the speed ratio of Champ and Hero is 3 : 1

So folks, you can avoid equations if you can put this reasoning into the question and I am sure this will be the quick way to solve this.

Let us look at the second question now

From the first question we have the speed ratio of Hercules, Hero and Champ as 3 : 2 : 6

Since, by the time Champ started Hero is 60 km ahead, Champ has to travel 60 km more than Hero in order to meet him. From their speeds ratio we can conclude that if Champ travels 90 km, in the same time Hero covers 30 km and thus Champ meets Hero after traveling 90 km. In the same time Hercules covers 45 kms.

Thus by the time Champ meets Hero, Hercules is 45 km ahead of them.

Let us suppose that 3x km be the distance that Hercules has to travel from here so that Champ is exactly in between Hero and Hercules.

If Hercules covers 3x km, in the same time Hero covers 2x km and Champ covers 6x km.

So now the distance between Hero and Champ is 4x km and the distance between Champ  and Hercules is (45 - 3x) km

Given that 4x = 45 - 3x

i.e x = 45/7 = 6.42 km.

The distance between Hero and Hercules is 45 + x = 51.42 km

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