A walk at a uniform rate of 4 km an hour; and 4 hr after his start, B bicycles after him at the uniform rate of 10 km an hour. How far from the starting point will B catch A ?

Solution(By Examveda Team)

Distance covered by A in hrs = (4 × 4) km = 16 km
Relative speed of B w.r.t. A = (10 - 4) km/hr = 6 km/hr
Time taken to cover 16 km at relative speed :
$$\eqalign{ & = \left( {\frac{{16}}{6}} \right){\text{ hrs}} \cr & = \frac{8}{3}{\text{ hrs}} \cr} $$
Distance covered by in $$\frac{8}{3}$$ hrs
$$\eqalign{ & = \left( {10 \times \frac{8}{3}} \right){\text{ km}} \cr & {\text{ = }}\left( {\frac{{80}}{3}} \right){\text{ km}} \cr & {\text{ = 26}}{\text{.7 km}} \cr} $$