how to calculate speed of two object that are moving toward each other?

Question

Two cars started their journey from point A and B 150 km apart on the same road towards each other.The car started from A traveled at a constant speed 10 km/hr more than that of hat also traveled at a constant speed.The two cars crossed each other after 72 minutes . What was the speed of car that started from point B .

What I have done is :

  S= 15km/h
  t=72mins *1/60= 5/6 hrs

Now

more than that of also traveled at a constant speed// "what does it mean"? is this mean this : VA= 10VB

So

 S=vt
150=VB*6/5------(1)

Since it is given

VA= 10VB
 therefore 
VB= VA/10

eq(1)=>150=VA/10*6/5

this way answer is not correct

Answer 1

Let $v_A$ be the speed of the car departing point $A$; let $v_B$ be the speed of the car departing point $B$. Since the speed of the car leaving point $A$ is $10$ km/h greater than that of the car leaving point $B$,

$$v_A = v_B + 10~\frac{\text{km}}{\text{h}}$$

Since there are $60$ minutes in an hour, $72$ minutes is

$$72~\text{min} \cdot \frac{1~\text{h}}{60~\text{min}} = \frac{6}{5}~\text{h}$$

Since the cars are initially $150~\text{km}$ apart and meet after $72$ minutes, the total combined distance traveled by the two cars in $72$ minutes is $150~\text{km}$. Thus,

\begin{align*} (v_A + v_B)t & = 150~\text{km}\\ \left(v_B + v_B + 10~\frac{\text{km}}{\text{h}}\right)\left(\frac{6}{5}~\text{h}\right) & = 150~\text{km}\\ \left(2v_B + 10~\frac{\text{km}}{\text{h}}\right)\left(\frac{6}{5}~\text{h}\right) & = 150~\text{km}\\ 2v_B + 10~\frac{\text{km}}{\text{h}} & = 125~\frac{\text{km}}{\text{h}}\\ 2v_B & = 115~\frac{\text{km}}{\text{h}}\\ v_B & = 57.5~\frac{\text{km}}{\text{h}}\\ \end{align*}

Answer 2

Car A:

• Initial position at $x_{0A}=0km.$
• Initial speed at $v_A = 10km/hr+v_B.$

Car B:

• Initial position at $x_{0B}=150km.$
• Initial speed at $v_B.$

After 72 minutes they crossed each other (this means they are in the same place after 72 minutes, i.e. $1.2hr$):
$x_A = 12km+1.2hr(v_B)$
$x_B = 150km- 1.2hr(v_B)$

Then: $$12km + 1.2hr(v_B) = 150km -1.2hr(v_B)$$ $$2.4hr(v_B) = 138km$$ $$v_B = 57.5km/hr$$ $$v_A = 67.5km/hr$$