Jeffrey K. answered • 08/12/20

Together, we build an iron base in mathematics and physics

Hi Savannah:

Here's the solution.

We need the standard equation: s = vt where s = distance traveled, v = average speed, t = time

Let Kaitlin's average speed on the way to the mountain be v => on the way back, average speed = v + 18

Let the distance to the mountains be s.

Plugging into the standard equation, on the way to the mountain s = 10 v . . . . . . . . . . . (1)

And on the way back s = 7 (v + 18) . . . . . . . . (2)

Substitute (1) into (2): 10v = 7(v + 18)

10v = 7v + 126

3v = 126

v = 42 mph

Substitute into (1): s = 10 x 42 = 420 miles

Check: 420 miles at 42 mph = 10 hours and 420 miles at 42 + 18 = 60 mph = 7 hours, as required.