#### Answer

a) Kentucky Derby race:
Length in:
$\Longrightarrow$ Rods = 400
$\Longrightarrow$ Furlong = 10
$\Longrightarrow$ Meters = 2011.68
$\Longrightarrow$ Kilometers = 2.01168
b) Marathon race:
Length in:
$\Longrightarrow$ Rods = 10,437.5
$\Longrightarrow$ Furlong = 260.9375
$\Longrightarrow$ Meter = 52,492.275
$\Longrightarrow$ Kilometer = 52.492275

#### Work Step by Step

a) Kentucky Derby race:
Length = 1.25 miles
1 mile = 8 furlongs
Thus, 1.25 miles = 10 furlongs
Also, 1 furlong = 40 rods.
Thus, 10 furlongs = 400 rods
1 mile = 1610 meter
Thus, 1.25 miles = 2011.68 meter
2011.68 m = 2.01168 km.
b) Marathon race:
Length = 26 miles, 385 yards.
1 mile = 8 furlongs
Thus, 26 miles = 208 furlongs
also, 5.5 yd = 1 rod
Thus, 385 yd = 2117.5 rods
40 rod = 1 furlong
2117.5 rods = 52.9375 furlong.
Total = 208 + 52.9375 = 260.9375 furlong.
In rods:
1 furlong = 40 rods
Thus, 260.9375 furlongs = 10437.5 rods
From (a), where 400 rods = 2011.68 meter,
1 rod = 5.0292 meter.
Thus 10437.5 rods = 52492.275 meter
Also, 52492.275 m = 52.492275 km.