A homing device left its home to deliver a message. On takeoff, the device encountered a tailwind of 10 mph and made the delivery in 15 minutes. The return trip into the wind took 30 minutes. How fast could the device fly in still air?

  30 miles per hour

Step-by-step explanation:

The relationship between time, speed, and distance is ...

  time = distance/speed

For some distance d and some speed s (in miles per hour), the travel times (in hours) are ...

  1/4 = d/(s+10)

  1/2 = d/(s -10)

Dividing the second equation by the first gives ...

  (1/2)/(1/4) = (d/(s-10))/(d/(s +10))

  2 = (s +10)/(s -10) . . . . simplify

  2s -20 = s +10 . . . . . . multiply by (s -10)

  s = 30 . . . . . . . . . . . add 20-s

  The device flies 30 miles per hour in still air.

__

Additional comment

The distance to the delivery point is ...

  d = 1/4(s +10) = 1/4(30 +10) = 10 . . . . miles to the delivery point

the image of (6, 9) under a dilation is (4, 6). the scale factor is