Mike is biking to catch up with his sister who is already 1200 yards ahead of him. If he bikes at a speed of 600 yards per minute and his sister is biking at a speed of 450 yards per minute, how long will it take for him to catch her?

8 minutes.

Step-by-step explanation:

Let m represent number of minutes.

We have been given that Mike is biking to catch up with his sister who is already 1200 yards ahead of him. His sister is biking at a speed of 450 yards per minute.

So total distance covered by Mike's sister after m minutes would be .

Mike bikes at a speed of 600 yards per minute, so total distance covered by Mike in minutes would be .

Now, we will equate both expressions to find minutes at which both distances will be equal as:

Therefore, it will take after 8 minutes for Mike to catch his sister.

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: