Question

X is travelling from city A to city B, while Y is making the same journey in opposite direction. Speed of X is twice of the speed of Y. They meet at point S after travelling for 2 hours and continue travelling to their respective destinations. The next day, X and Y do the return journey. Y starts 36 minutes earlier, while X starts 24 minutes late. If they meet 24 Km from S, what is the distance between the two cities? *

Answer 1

Step-by-step explanation:

Let speed of car starting from A=x km/hr and speed of car starting from B=y km/hr.

Relative speed of A with respect to B when moving in same direction =x−y km/hr.

Relative speed of A with respect to B when moving in opposite direction =x+y km/hr.

Distance between A and B=100 km.

We know, Time=

Speed

Distance

From the above information, we have,

x−y

100

=5and

x+y

100

=1

or,

x−y

100

=5

=>100=5(x−y)

=>20=x−y

=>x=y+20....(i)

Also,

x+y

100

=1

=>100=x+y

=>x+y=100....(ii)

By substitution method,

Substituting equation (i) in equation (ii), we get,

x+y=100

=>y+20+y=100

=>2y=80

=>y=40

Substituting y=40 in equation (i), we get,

x=y+20

=>x=40+20

=>x=60

Thus, speed of car starting from A=x=60 km/hr and speed of car starting from B=y=40 km/hr.

Answer 2

Given: X is travelling from city A to city B, while Y is making the same journey in opposite direction.

To find: Distance between two cities.

Solution:

Let speed of car starting from $A=x km/hr$ and speed of car starting from $B=y km/hr$.

Relative speed of A with respect to B when moving in same direction $=x-y km/hr.$

Relative speed of A with respect to B when moving in opposite direction $=x+y km/hr.$

Distance between A and B$=100 km.$

Know that, $\[{\rm{Time = }}\frac{{{\rm{Distance}}}}{{{\rm{Speed}}}}\]$

Form the equations according to the conditions given in the question.

$\[\frac{{100}}{{x - y}} = 5\]$

$\[\begin{array}{l} \Rightarrow 100 = 5\left( {x - y} \right)\\ \Rightarrow 20 = x - y\\ \Rightarrow x = y + 20------(1)\end{array}\]$

Also,

$\[\frac{{100}}{{x + y}} = 1\]$

$\[\begin{array}{l} \Rightarrow 100 = x + y\\ \Rightarrow x + y = 100------(2)\end{array}\]$

 Solve equation (1) and (2) by substitution method,

Substitute equation (i) in equation (ii),  

$\[\begin{array}{l}x + y = 100\\ \Rightarrow y + 20 + y = 100\\ \Rightarrow 2y + 20 = 100\end{array}\]$

$\[\begin{array}{l} \Rightarrow 2y = 100 - 20\\ \Rightarrow 2y = 80\end{array}\]$

$\[ \Rightarrow y = \frac{{80}}{2}\]$

$\[ \Rightarrow y = 40km/hr\]$

Substitute $y=40 km/hr$ in equation (i),  

$\[\begin{array}{l}x = y + 20\\ \Rightarrow x = 40 + 20\\ \Rightarrow x = 60km/hr\end{array}\]$

Hence, speed of car starting from A is 60 km/hr, and the speed of car starting from B is40 km/hr.