Question

Places $A$ and $B$ are $100km$ 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 $10$ hours and if they move in opposite directions they meet in $1$ hour $40$ minutes. Find the speed of the cars from places A and B, respectively.

• A. $45km/hr,25km/hr$
• B. $65km/hr,75km/hr$
• C. $35km/hr,25km/hr$
• D. $60km/hr,45km/hr$

Answer 1

The correct option is C $35km/hr,25km/hr$

Let A and B be two cars starting from points A and B respectively.

Let the speed of the car A be $x$ km/hr and that of car B be $y$ km/hr.

The relative speed of car A & B is $x-y$ when they move in the same direction and

$x+y$ when they move in the opposite direction.

Now, the time taken to cover AB in the first case is

$\frac{distance}{speed}=\frac{100}{x-y}=10⟹x-y=\mathrm{10......}\left(i\right).$

In the second case, the time taken to cover AB is

$\frac{distance}{speed}=\frac{100}{x+y}hr=1hr40min=1\frac{2}{3}hr=\frac{5}{3}hr⟹5x+5y=300⟹x+y=\mathrm{60.......}\left(ii\right).$

Adding (i) & (ii),

$2x=70$

$\therefore x=35\frac{km}{hr}.$

Putting this value of x in (i),

$y=x-10=35-10=25.$

$\therefore y=255\frac{km}{hr}.$

The speed of car A is $x=35\frac{km}{hr}.$ and

The speed of car b is $y=25\frac{km}{hr}.$

Ans- Option C.