Question

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Janet and Michelle begin walking at the same time from the same point. Janet walks directly north, and Michelle walks directly ea
10 km apart, Michelle has walked 2 km farther than Janet has walked. How far has Michelle walked?
08 km
06 km
12 km
10 km

Answer 1

9514 1404 393

Answer:

  (a)  8 km

Step-by-step explanation:

Let m represent the distance (in kilometers) Michelle has walked. Then Janet walked a distance of (m-2). These distances are at right angles, so the distance between them can be found using the Pythagorean theorem.

  m² +(m -2)² = 10²

  m² +m² -4m +4 = 100

  2m² -4m = 96 . . . . . . subtract 4, collect terms

  m² -2m +1 = 49 . . . . . divide by 2 and add 1

  (m -1)² = 7² . . . . . . .write as squares

  m -1 = 7 . . . . . . positive square root

  m = 8

Michelle walked 8 km.