Question

Places A and B are 160 km apart on a highway. One car starts from A and another car from B at the same time. If they travel in the same direction , they meet in 8 hours. But, if they travel towards each other, they meet in 2 hours. Find the speed of each car.

Answer 1

Let the speed of the car A and B be x km/h and y km/h respectively . Let x > y.
Case-1: When they travel in the same direction

From the figure
$$\begin{gathered} AC-BC=160 \\ \Rightarrow x\times 8-y\times 8=160 \\ \Rightarrow x-y=20.....\left(i\right) \end{gathered}$$
Case-2: When they travel in opposite direction

From the figure
$$\begin{gathered} AC+BC=160 \\ \Rightarrow x\times 2+y\times 2=160 \\ \Rightarrow x+y=80.....\left(ii\right) \end{gathered}$$
Adding (i) and (ii), we get
$2x=100\Rightarrow x=50\mathrm{km}/\mathrm{h}$
Putting x = 50 in (ii), we have
$50+y=80\Rightarrow y=80-50=30\mathrm{km}/\mathrm{h}$
Hence, the speeds of the cars are 50 km/h and 30 km/h.