Answer
Walking to the lab burns more energy. Walking to the lab uses $1.7\times 10^6 J$ of energy. Although walking uses less power as it is less intense, walking lasts significantly longer than running, so walking ends up burning more energy than running.
Work Step by Step
We can find the time it takes to run to the lab.
$t = \frac{d}{v} = \frac{5.0~km}{10~km/h} = 0.5 ~hours$
We can find the energy used in running to the lab.
$E = P~t = (700~W)(1800~s) = 1.3\times 10^6 J$
We can find the time it takes to walk to the lab.
$t = \frac{d}{v} = \frac{5.0~km}{3.0~km/h} = \frac{5.0}{3.0} ~hours$
We can find the energy used in walking to the lab.
$E = P~t = (290~W)(6000~s) = 1.7\times 10^6 J$
Walking to the lab burns more energy. Walking to the lab uses $1.7\times 10^6 J$ of energy. Although walking uses less power as it is less intense, walking lasts significantly longer than running, so walking ends up burning more energy than running.
