Time, Speed & Distance

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$A$ and $B$ start running simultaneously. $A$ runs from point $P$ to point $Q$ and $B$ from point $Q$ to point $P$. $A$'s speed is 6/5 of $B$'s speed. After crossing $B$, if $A$ takes 5/2 hr to reach $Q$, how much time does $B$ take to reach $P$ after crossing $A$?


3 hr 6 min


3 hr 16 min


3 hr 26 min


3 hr 36 min

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Option(D) is correct


\(\begin{align*} \dfrac{V_A}{V_B}=\sqrt{\left(\dfrac{t_B}{t_A}\right)}\\ \Rightarrow \left(\dfrac{6}{5}\right)^2=\dfrac{t_B}{t_A}\\ t_B=\dfrac{36}{25}\times \dfrac{5}{2}\\ \end{align*}\)

= 3.6 hour 
3 hr 36 min

(2) Comment(s)


the solution would be like this

let A and b meet at point X, distance between them is say D. so distance a has to travel is X , while distance for B to travel is D-X, therefore time taken by A should be equal to time taken by B.

which can be expressed as

X/Sa = D-X/Sb ........(1)

we know Sa/Sb=6/5......(2)

so X/D-X = 6/5 ........(3)

remaining time taken by A to travel (D-X) distance is

Ta = D-X/Sa = 5/2 ......(4)

which is given

so remaining diatance to be covered by B is X which should be covered in Tb min

Tb= X/Sb

now substitute the value of 2 and 3 in equation 4 , you would be getting the equation as



can anyone please explain the solution in detail