Question

Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and If they move in the opposite directions, they meet 1 hour and 20 minutes. Find the speeds of the cars.

Answer 1

Let the speed of car starting from A be ${}^{\prime }{x}^{\prime }km/h$ and speed of car starting from B be ${}^{\prime }{y}^{\prime }km/h.$

Total distance $=80km$

Also 1 hour 20 mins $=1+\frac{20}{60}$ hours $=1+\frac{1}{3}$ hours $=\frac{4}{3}$ hour

As per given condition, When car moves in same direction they will meet in 8 hours.

Distance travelled from B $=8ykm$ [$\because$ Distance $=$ Speed $\times$ Time]

Distance travelled from A $=8x$

Now, Equation formed is

$\Rightarrow 8x-8y=80$ [Difference between the distance covered by the two cars $=80km$]

$\Rightarrow x-y=\mathrm{10.......}\left(i\right)$

Similarly, When car moves in opposite direction they will meet in 1 hour 20 mins.

Distance travelled from A $=\frac{4x}{3}$

Distance travelled from B $=\frac{4y}{3}$

Also total distance covered $=\frac{4x}{3}+\frac{4y}{3}$

$80=\frac{4x}{3}+\frac{4y}{3}$

$\Rightarrow 240=4x+4y$

$\Rightarrow 60=x+y.......\left(ii\right)$

on adding Equation (i) and eq. (ii), we get

$x+y+x-y=60+10$

$\Rightarrow x=35$

Substituting the value of x in (ii) we get

$60=35+y$

$\Rightarrow y=60-35=25$

Therefore Speed of car starting from A is $35km/h$

Speed of car starting from B is $25km/h$