A circular field has a circumference of 360 km.Three cyclists start together and and can cycle 48,60 and 72 km a day round the field when will they meet again. Full explanation?

Question

Answer

Problem:

A circular field has a circumference of 360 km. Three cyclists start together and can cycle 48, 60, and 72 km a day round the field. When will they meet again?

Solution:

Let's solve this problem step by step.

Find the time taken by each cyclist to complete one round of the field:

The circumference of the field is 360 km. Therefore, the time taken by each cyclist to complete one round of the field can be calculated as follows:

Cyclist 1: 360/48 = 7.5 days

Cyclist 2: 360/60 = 6 days

Cyclist 3: 360/72 = 5 days

Find the LCM of the above time periods:

The LCM of 7.5, 6, and 5 is 30. Therefore, the three cyclists will meet again after 30 days.

Calculate the number of rounds completed by each cyclist in 30 days:

The number of rounds completed by each cyclist in 30 days can be calculated as follows:

Cyclist 1: 30/7.5 = 4 rounds

Cyclist 2: 30/6 = 5 rounds

Cyclist 3: 30/5 = 6 rounds

Find the distance covered by each cyclist in 30 days:

The distance covered by each cyclist in 30 days can be calculated by multiplying the number of rounds completed by each cyclist by the distance covered in one round:

Cyclist 1: 4 x 360 = 1440 km

Cyclist 2: 5 x 360 = 1800 km

Cyclist 3: 6 x 360 = 2160 km

Find the common point where all three cyclists meet:

The common point where all three cyclists meet can be calculated by finding the common multiple of the distances covered by each cyclist in 30 days. The common multiple of 1440, 1800, and 2160 is 10,800 km.

Find the number of days taken to cover 10,800 km:

The number of days taken by the three cyclists to cover 10,800 km can be calculated as follows:

Total distance covered by the three cyclists in one day = 48 + 60 + 72 = 180 km

Number of days taken to cover 10,800 km = 10,800/180 = 60 days

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