Anne , Sunil and Jose were practising for a hurdle race .Anne crosses a hurdle after every 20m ,Sunil after every 25m and Jose after every 30m.If their starting and finishing points are the same , how many hurdles will each person cross? Also , find the distance between the starting point and the finishing point.
Answers
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The number of hurdles is 5 and The Distance between the Starting point and the Finishing point is 300m.
Given:
- Anne crosses a hurdle after every 20m
- Sunil crosses a hurdle after every 25m
- Jose crosses a hurdle after every 30m
To find:
The number of hurdles will cross by each person and the Distance between the Starting point and the Finishing point.
Solution:
We can simply solve this question by using the following question.
Now, we have
Anne, Sunil, and Jose cross a hurdle after every 20m,25m, and 30m respectively.
So, we can say
The number of hurdles = HCF of Anne, Sunil, and Jose's time to cross a hurdle.
So, the factors of 20,25, and 30 is
20 = 2 × 2 × 5
25 = 5 × 5
30 = 5 × 3 × 2
So, the HCF of 20, 25, and 30 is 5.
∴ The number of hurdles is 5.
Now, to calculate the distance between the starting point and the finishing point we can do,
The Distance between the Starting point and the Finishing point = LCM of HCF of Anne, Sunil, and Jose's time to cross a hurdle.
So, the factors of 20,25, and 30 is
20 = 2 × 2 × 5
25 = 5 × 5
30 = 5 × 3 × 2
So, the LCM of 20,25, and 30
= 2 × 2 × 3 × 5 × 5
= 12 × 25
= 300
∴ The Distance between the Starting point and the Finishing point is 300m.
Hence, The number of hurdles is 5 and The Distance between the Starting point and the Finishing point is 300m.
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