Question

At noon, ship A starts from a point P towards a point Q and at 1.00 pm ship B starts from Q towards P. If the ship A is expected to complete the voyage in 6 hours and ship B is moving at a speed $\frac{2}{3}$ that of ship A, at what time are the two ships expected to meet one another ?

• A. $4pm$
• B. $4.30pm$
• C. $3pm$
• D. $2.30pm$

Answer 1

The correct option is A $4pm$

let the distance between A & B be $x$ km.

A covers this distance in $6hrs.$

$\therefore$ The speed of A=$\frac{x}{6}$ and

as given, the speed of B=$\frac{x}{6}\times \frac{2}{3}=\frac{x}{9}$ .
We know that if two ships proceed in opposite directions then their relative speed will be the sum of their speeds.

$\therefore$ The relative speed of A & B=$\frac{x}{6}+\frac{x}{9}=\frac{5x}{18}$..........(i).

Now A starts at 12 noon and B starts at 1 pm.

So in 1 hr A covers a distance=$\frac{x}{6}$.

Rest of the distance=$x-\frac{x}{6}=\frac{5x}{6}$.

So, the time taken by the ships to cover this distance in order to meet

=distance/relative speed

=$\frac{5x}{6}÷\frac{5x}{18}=\frac{5x}{6}\times \frac{18}{5x}=3$ hrs.

Now $1pm+3hrs=4pm.$

So the ships will meet one another by $4pm.$