Question

Points A and Bare 80 km. apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in one hour and twenty minutes. Find the speeds of the two cars

• A. 55 km/h & 35 km/hr
• B. 50 km/h & 35 km/hr
• C. 70 km/h & 60 km/hr
• D. 35 km/h & 25 km/hr

Answer 1

Answer: (D)

35 km/h & 25 km/hr

Let the speed of car starting from point A=x km/hr

The speed of car starting from point B=y km/hr

According to the first condition :The two cars travel in same direction-

$speed\Rightarrow (x-y)\frac{km}{hr}$

$\because speed=\frac{distance}{time}$

$\Rightarrow x-y=\frac{80}{8}\Rightarrow x-y=\mathrm{10....}eq1$

According to the second condition :The two cars travel in opposite direction-

$\because speed=\frac{distance}{time}$

$\Rightarrow x+y=\frac{80}{\frac{4}{3}}\Rightarrow x+y=\mathrm{60....}eq2$

Adding eq1 and eq2

$\Rightarrow 2x=70\Rightarrow x=35$

put $x=35$ in eq1

$\Rightarrow 35-y=60\Rightarrow y=25$

Hence, the speed of car starting from point A=35km/hr

The speed of car starting from point B=25 km/hr