Answer
The fractional difference between Method 1 and Method 2 is $\frac{9}{15616}$
Work Step by Step
$$ v_{foreward (f)} = v_{c} + v_{w} $$
$$ v_{backward (b)} = v_{c} - v_{w} $$
$$ t_{f} = \frac{d}{v_{f}} $$
$$ t_{b} = \frac{d}{v_{b}} $$
Method 1
$$ v_{avg} = \frac{\frac{d}{t_{f}} + \frac{d}{t_{b}}}{2} $$
Method 2
$$ v_{avg} = \frac{d}{\frac{t_{f} + t_{b}}{2}} $$
Since $ v_{w} = 0.0240 v_{c} $ :
$$ v_{f} =1.024 v_{c} $$
$$ v_{b} = 0.976 v_{c} $$
M1:
$$v_{avg} = \frac{(1.024 + 0.976) v_{c}}{2} = v_{c}$$
M2:
$$v_{avg} = \frac{d}{\frac{\frac{d}{1.024v_{c}} + \frac{d}{0.976v_{c}}}{2}} = \frac{d}{\frac{\frac{15625 d}{7808 v_{c}}}{2}} = \frac{15625}{15616} v_{c}$$
$$ v_{avg_{M2}} - v_{avg_{M1}} = \frac{15625}{15616} - 1 = \frac{9}{15616} $$
