#### Answer

The cyclist must bike for $5.05 hours$

#### Work Step by Step

First we must convert the speed of $84 miles/hr$ to kilometers/hr. Using the conversion factor $1 mile/hr$ $=$ $1.60934 km/hr$, we can find that $24 mi/hr$ $=$ $38.6243 km/hr$ because:
$$24 mi/hr\times\frac{1.60934 km/hr}{1 miles/hr} = 38.6243 km/hr$$
Next since we know that time = distance/velocity we can take the distance of 195 km and divide by the velocity or speed of 38.6243 to get a time of roughly $5.05 hours.$