Dana can run at a rate of speed four times faster than she can walk, but she can skip at a rate of speed that is half as fast as she can run. If she can skip at 3 miles per hour, how many miles can she travel in six hours if she spends one-third of the time running and two-thirds of the time walking?
If Dana can skip at half the speed she can run, then she can run at 3*2=
<gadget id="calculator">3*2</gadget>
<output>6</output>
6 miles per hour.
And since she can run at a speed that is 4 times faster than she can walk, this means she can walk at 6/4=1.5 miles per hour.
If two-thirds of the time is spent walking, then she walks for 6*(2/3)=
<gadget id="calculator">6*(2/3)</gadget>
<output>4</output>
4 hours.
If one-third of the time is spent running, then she runs for 6-4=
<gadget id="calculator">6-4</gadget>
<output>2</output>
2 hours.
Thus, she runs for 2 hours at 6 miles per hour, or 2*6=
<gadget id="calculator">2*6</gadget>
<output>12</output>
12 miles.
She walks for 4 hours at 1.5 miles per hour, or 4*1.5=
<gadget id="calculator">4*1.5</gadget>
<output>6</output>
6 miles.
Thus, altogether, she travels 12+6=
<gadget id="calculator">12+6</gadget>
<output>18</output>
18 miles.

<result>18</result>