X, y, z starts at the same time in the same direction to run around a circular stadium x complete a round in 126 seconds, y in 154 seconds and z in 231 seconds. After what time they meet again at the starting point and how many rounds would have x, y, z complete by this time?

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Answer

Problem:

X, y, z starts at the same time in the same direction to run around a circular stadium x complete a round in 126 seconds, y in 154 seconds and z in 231 seconds. After what time they meet again at the starting point and how many rounds would have x, y, z complete by this time? Explain in details.

Solution:

Let's assume that they meet after t seconds and in that time they complete n rounds.

Calculating the speed of each person:

Speed of x = Distance/Time = 1/126

Speed of y = Distance/Time = 1/154

Speed of z = Distance/Time = 1/231

Calculating the distance of the round:

As they complete full rounds, the distance covered by each person is equal to the circumference of the stadium.

Circumference of the stadium = 2πR, where R is the radius of the stadium.

Let's assume the radius of the stadium to be 'r'.

Circumference of the stadium = 2πr

Distance covered by x in one round = 2πr

Distance covered by y in one round = 2πr

Distance covered by z in one round = 2πr

Calculating the number of rounds:

As each person completes 'n' rounds, we can say that:

Distance covered by x = n * 2πr

Distance covered by y = n * 2πr

Distance covered by z = n * 2πr

Calculating the time taken:

As each person completes 'n' rounds in 't' seconds, we can say that:

Time taken by x = n * 126 seconds

Time taken by y = n * 154 seconds

Time taken by z = n * 231 seconds

Calculating the value of 'n' and 't':

As they meet at the starting point after 't' seconds, we can say that:

Distance covered by x in 't' seconds = Distance covered by y in 't' seconds = Distance covered by z in 't' seconds

Therefore, we can say that:

n * 2πr = (n * 1/126) * t * 2πr = (n * 1/154) * t * 2πr = (n * 1/231) * t * 2πr

Cancelling out 2πr from both sides, we get:

n = (t/126) = (t/154) = (t/231)

Answer

They will meet after 1386 seconds by this time X will complete 11 rounds Y 9 rounds and Z 6 rounds. You can find the time they will meet again by taking l.c.m  of 126 , 154 and 231 and to find rounds completed by x, y and z by dividing l.c.m. by 126, 154 and 231 respectively

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Plz answer me

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