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ohaa [14]
3 years ago
9

Two cyclists, Alan and Brian, are racing around oval track of length 450m on the same direction simultaneously from the same poi

nt. Alan races around the track in 45 seconds before Brian does and overtakes him every 9 minutes. What are their rates, in meters per minute?
Mathematics
1 answer:
Ksenya-84 [330]3 years ago
6 0

Answer:

  • Alan: 200 m/min
  • Brian: 150 m/min

Step-by-step explanation:

Let n represent the number of laps that Alan completes in 9 minutes. Then n-1 is the number of laps Brian completes, and the difference in their lap times in minutes per lap is ...

  9/(n -1) - 9/n = 3/4 . . . . . minutes

Multiplying by (4/3)n(n -1), we get

  12n -12(n -1) = n(n -1)

  12 = n(n -1)

Solutions to this are n=4 and n=-3. We are only interested in the positive solution, n = 4. Then Alan's speed in m/min is ...

  (4·450 m)/(9 min) = 200 m/min

Brian completes 3 laps in that 9-minute time, so his rate is ...

  (3·450 m)/(9 min) = 150 m/min

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8 0
3 years ago
Kate gave 5/6 of her CDs to Sue. Sue gave 7/8 of these to Joan. Joan gave 3/5 of these to Ann. Ann received 70 CDs how many did
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Let us assume the number of CDs Kate had = x
Number of CDs given to Sue = 5x/6
Number of CDs given to Joan = (5x/6) * ( 7/8)
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Then
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5 0
4 years ago
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8 0
3 years ago
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KATRIN_1 [288]
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7 0
4 years ago
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