Two sisters leave their house at the same time, and walk in opposite directions. In five hours they are exactly 30 miles apart. Find their speeds given that the older sister travels twice as fast as the younger sister.

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Step-by-step explanation:

Since the sisters are walking in opposite directions, the amount of distance between them increases at a rate equal to their combined walking speeds. That rate is ...

  speed = distance/time

  speed = (30 mi)/(5 h) = 6 mi/h

If y represents the speed of the younger sister, their combined speeds are ...

  y +2y = 6

  3y = 6

  y = 6/3 = 2 . . . . . . . younger sister's speed

  2y = 2(2) = 4 . . . . . older sister's speed

The older sister's speed is 4 miles per hour; the younger's speed is 2 miles per hour.