Question

Points $A$ and $B$ are $90km$ apart from each other on a highway. A car starts from $A$ and another from $B$ at the same time. If they go in the same direction, they meet in $9hrs$ and if they go opposite directions, they meet in $\frac{9}{7}hrs$. Find their speeds.

• A. The speed of car starting from point $A=30km/hr$ and speed of car starting from point $B=550km/hr$.
• B. The speed of car starting from point $A=60km/hr$ and speed of car starting from point $B=40km/hr$.
• C. The speed of car starting from point $A=40km/hr$ and speed of car starting from point $B=30km/hr$.
• D. The speed of car starting from point $A=25km/hr$ and speed of car starting from point $B=20km/hr$.

Answer 1

The correct option is C The speed of car starting from point $A=40km/hr$ and speed of car starting from point $B=30km/hr$.

Let the speeds of the cars starting from A xkm/hr and B be y km/hr respectively.
Let us assume that speed of car A is greater than B
Case 1
Distance covered by car A in 9 hours $=$ 90km + Distance covered by car B in 9 hours
We know Distance $=$ Speed *Time
$\Rightarrow$xkm/hr*9hrs $=$ 90km + ykm/hr*9hrs
$\Rightarrow$9x $=$ 90 +9y
$\Rightarrow$9x-9y $=$ 90
$\Rightarrow$x - y $=$ 10.....(1)
Case2
Distance covered by car A in 9/7 hours + Distance covered by car B in 9/7 hours $=$ 90km
$\Rightarrow$xkm/hr*$\frac{9}{7}$hrs+ ykm/hr*$\frac{9}{7}$hrs $=$90km
$\Rightarrow \frac{9}{7}x+\frac{9}{7}y=90$
$\Rightarrow$9x+9y$=$ 630
$\Rightarrow$x+y $=$ 70..........(2)
Adding eq(1) and eq(2) we get
2x $=$ 80
$\Rightarrow$ x $=$ 40
Putting the value of x in eq(2) we get y $=$ 30
Hence the speed of car starting from point A=40km/hr and speed of car starting from point B=30km/hr.