Question

A naval ship can fire a torpedo at 200 mph every minute. If so, calculate the shortest time in which all three pirate ships shown in the image below will be hit. (Each rung in the graph represents a distance of 5 miles.)
(Calculate the time from the firing of the first torpedo to the hit of the last pirate ship.)

• A. 4.5 minutes
• B. 9 minutes
• C. 6 minutes
• D. 7.5 minutes

Answer 1

The correct option is A 4.5 minutes

$Speedofthetorpedo=200mph$

Calculating the time taken for the torpedo to hit each pirate ship once launched, we get:

$Pirateship1:Distancefromnavalship=5milesTimetakenbythetorpedo=\frac{Distance}{Speed}=\frac{5}{200}h=\frac{1}{40}\times 60min=1.5min$

$Pirateship2:Distancefromnavalship=10milesTimetakenbythetorpedo=\frac{Distance}{Speed}=\frac{10}{200}h=\frac{1}{20}\times 60min=3min$

$Pirateship3:Distancefromnavalship=15milesTimetakenbythetorpedo=\frac{Distance}{Speed}=\frac{15}{200}h=\frac{3}{40}\times 60min=4.5min$

As the naval ship has to shoot down the pirates in the shortest time possible, it has to shoot the farthest pirates first.

Hence, the 3rd pirate ship will be shot first, followed by the 2nd and the 1st.

$Totalnumberoftorpedosshot=3Timelagafterthe1sttorpedo=1minTimelagafterthe2ndtorpedo=1min⟹Totaltimelag=2min$

So, after 2 minutes, all 3 torpedos will have been shot.

Assessing the situation 2 minutes after the 1st shot, we find:


We find that the last pirate ship to be hit will be ship number 3 as it will go down only 2.5 minutes after the last shot has been fired.

Hence, the time between the 1st torpedo fired and the last ship hit will be:

$2min+2.5min=4.5min$