Question

A truck left the station at $6\mathrm{A}.\mathrm{M}.$ traveling at a rate of $45\mathrm{km}/\mathrm{h}$. A van left the same place $2\mathrm{hours}$ later heading in the same direction at a rate of $54\mathrm{km}/\mathrm{h}$. At what time will the van catch up with the truck?

Answer 1

The time when the van will catch up with the truck:

• Since the truck left the station at $6\mathrm{A}.\mathrm{M}.$traveling at a rate $45\mathrm{km}/\mathrm{h}$, and a van also left the same station $2$ hrs later in the same direction at a rate $54$ km/h.
• The truck has $2\mathrm{hours}$ ahead starts moving at $45\mathrm{km}/\mathrm{h}$ so it should be $90\mathrm{km}$ ahead.
• Let $t$ be the time taken by van to catch up with truck after $8\mathrm{A}.\mathrm{M}.$ so the distance should be $\mathrm{d}=90+45\mathrm{t}$ and $\mathrm{d}=54\mathrm{t}$

Now, Equate the distance to calculate the time van will take to catch up with truck:

$\begin{array}{rcl}54t& =& 90+45t\\ & \Rightarrow & 9t=90\\ & \Rightarrow & t=10\end{array}$

Thus, the van will take $10$ hrs to catch up with the truck, the exact time will be $(6\mathrm{AM}+2\mathrm{hrs}+10\mathrm{hrs})=6\mathrm{PM}$.