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Ahat [919]
3 years ago
10

two bike riders ride around in a circular path. The first rider completes one round in 15 minutes and the second rider completes

it in 18 minutes. if they both start together and ride the same route, after how many minutes will they meet again at the starting place​
Mathematics
1 answer:
katrin2010 [14]3 years ago
3 0

Answer:

Rider 1 does one round in 15 min, and will complete another in each consecutive multiple of 15 min

Rider 2 does one round in 18 min, and will complete another in each consecutive multiple of 18 min

Assuming that they start together, they will complete another round together in a time that is both multiples of 15min and 18 min.

Then we need to find the smallest common multiple between 15 and 18.

To smallest common multiple between two numbers, a and b, is equal to:

a*b/(greatest common factor between a and b).

Now, the greatest common factor between 15 and 18 can be found if we write those numbers as a product of prime numbers, such as:

15 = 3*5

18 = 2*3*3

The greatest common factor is 3.

Then the smallest common multiple will be:

(15*18)/3 = 90

This means that after 90 mins, they will meet again at the starting place.

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First, we are going to find the conjugate of our complex number. Remember that to find the conjugate of a complex number we just need to keep the real part and change the sing of the imaginary part.

We can infer from our problem that the real part of our complex number is 3 and its imaginary part is 3i. We are going to keep the real part 3 and change the imaginary part from positive to negative, so our conjugate is 3-3i.

Next, we are gong to multiply both the complex number and its conjugate using the distributive property:

(3+3i)(3-3i)=(3*3)-(3*3i)+(3*3i)-(3i*3i)=9-9i+9i-9i^2=9-9i^2

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