1 ) Lamp posts,dust bins and benches are paced at intervals of 70 m ,56 m ,and 84 m respectively along a strech of road 8km long.At start of the road,lamp post,dust bin and bench are placed together.Only when the three objects are all placed together,they are painted blue.
How far away from the start of the road are the second set of the 3 blue object spotted ?
What is the LCM of the three distances?
in the question doesn't write.
so , we find the LCM or HCF ?
To find the distance from the start of the road where the second set of the three blue objects is spotted, we need to find the least common multiple (LCM) of the intervals between the objects.
First, let's convert the road length to meters:
8 km = 8,000 meters
Next, we need to find the LCM of 70 m, 56 m, and 84 m.
To find the LCM, we can list the multiples of each interval and find the smallest common multiple:
Multiples of 70 m: 70, 140, 210, 280, 350, 420,...
Multiples of 56 m: 56, 112, 168, 224, 280, 336, 392,...
Multiples of 84 m: 84, 168, 252, 336, 420, 504,...
From the list, we can see that the smallest common multiple of 70, 56, and 84 is 280 meters.
Now, we can calculate how many sets of the three objects are placed along the 8,000-meter road:
Number of sets = road length / LCM = 8,000 m / 280 m = 28.57
Since we can't have a fraction of a set, we can round down to the nearest whole number. Therefore, there are 28 sets of the three objects along the road.
To find the distance from the start of the road where the second set of the three blue objects is spotted, we multiply the LCM by the number of sets:
Distance = LCM * (n-1) = 280 m * (2-1) = 280 meters
So, the second set of the three blue objects is spotted 280 meters away from the start of the road.