Question

Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B at the same time.if they travel in same direction, they meet in 7 hours, but if they travel in opposite direction, they meet in one hour.Then the speeds of the cars are.......

Answer 1

Given :-

• Distance between points A & B = 70 km.
• Time taken for the cars to meet together while travelling in the same direction = 7 hours.
• Time taken for the cars to meet while travelling in opposite direction = 1 hour.

To Find :-

• Speed of the two cars.

Solution :-

Let X and Y be the two cars starting from points A and B respectively. Let the speed of car X be x km/hr and that of car Y be y km/hr.

CASE I When two cars move in the same directions:

Suppose two cars meet at point Q. Then,

• Distance travelled by car X = AQ
• Distance travelled by car Y = BQ

It is given that two cars meet in 7 hours.

Therefore,

• Distance travelled by car X in 7 hours (AQ) = 7x km
• Distance travelled by car in Y in 7 hours (BQ) = 7y km.

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\put(0,0){\line(1,0){99}}\multiput(0,0)(33,0){4}{\circle*{1}}\put(-4,-5){A}\put(32,-5){P}\put(65,-5){B}\put(99,-5){Q}\put(24,4){\vector(-1,0){24}}\put(37,4){\vector(1,0){29}}\put(25,3){70\ km}\end{picture}$

From the figure, it is clear that AQ - BQ = AB

$\implies\rm{7x-7y=70\quad\quad\quad[{\because}\:AB=70\:km]}$

$\implies\rm{x-y=10\longrightarrow{(1)}}$

$\hrulefill$

CASE II When two cars move in opposite directions :

Suppose two cars meet at point P. Then,

• Distance travelled by car X = AP
• Distance travelled by car Y = BP

Here, it is given that the two cars meet in 1 hour.

Therefore,

• Distance travelled by car X in 1 hour (AP) = x km
• Distance travelled by car Y in 1 hour (BP) = y km

Again, AP + BP = AB

$\implies\rm{x+y=70\longrightarrow{(2)}}$

Adding ( 1 ) and ( 2 ), we get,

$\implies\rm{2x=80}$

$\implies\rm{x=\dfrac{80}{2}}$

$\implies\rm{x=}\:\bold{40}$

Substituting the value of x in ( 1 ) gives,

$\implies\rm{40-y=10}$

$\implies\rm{y=40-10=}\:\bold{30}$

Hence,

• Speed of car X = 40 km/hr.
• Speed of car Y = 30 km/hr.