Question 9701
If she ran and walked, she must have a running speed and a walking speed. Let's call these R and W, running and walking respectively.


They tell us that her running speed is double her walking speed. That translates to {{{ R = 2W }}}. The running speed is already faster. It makes sense to "inflate" the slower walking speed by multiplying it by 2 to match the running speed.


We are going to use that formula rate x time = distance, keeping in mind that we have to add up her walking distance and running distance to cover the total 12 miles. Her walking distance would be {{{ 2W }}} because she would be walking at W mph for two hours. Her running distance would be {{{ 0.5(2W) }}}. Remember that we have the relationship {{{ R = 2W }}} so we simply replaced the R with a 2W in the running distance expression. The 0.5 would be equivalent to the 30 minutes. Since we're working with hours and miles per hour, we need to convert the minutes to hours.


{{{ 2W + 0.5(2W) = 12 }}} <------- Start


{{{ 2W + W = 12 }}} <---- simplify


{{{ 3W = 12 }}} <---- combine like terms


{{{ W = 4 }}} <---- Her walking speed is 4 mph. If her running speed was double that, the running speed would be 8 mph.