Question

A ship can cover a certain distance in 10 hours at a speed of 16 nautical miles per hour. By how much should its speed be increased so that it takes only 8 hours to cover the same distance?

Answer 1

Hint: Start by finding the distance that the ship have to cover using the formula $ \text{distance=speed }\!\!\times\!\!\text{ time} $ and the statement that it takes 10 hours to cover a certain distance at the speed of 16 nautical miles per hour. Let the increment in the speed for the second case be x nautical miles per hour. Again use the same formula $ \text{distance=speed }\!\!\times\!\!\text{ time} $ to get the distance in terms of x nautical miles per hour and 8 hours’ time. Equate the distance in both results and solve to get the value of x.

Complete step-by-step answer:
Let us start the solution to the above question by finding the distance using the formula $ \text{distance=speed }\!\!\times\!\!\text{ time} $ . It is given that in the first case, the ship takes 10 hours to travel at the speed of 16 nautical miles per hour.
 $ \text{distance}=\text{speed }\!\!\times\!\!\text{ time}=16\times 10=160\text{ nautical miles}\text{.} $
Let the increment in the speed for the second case be x nautical miles per hour. So, the increased speed is (16+x) nautical miles per hour. Again using the formula $ \text{distance=speed }\!\!\times\!\!\text{ time} $ , with time to be taken be 8 hours in this case, we get
  $ \text{distance}=\text{speed }\!\!\times\!\!\text{ time}=\left( 16+x \right)\times 8 $
The distance still remains the same as the first case, so we will substitute the value of distance using the first case. On doing so, we get
 $ 160=\left( 16+x \right)\times 8 $
 $ \Rightarrow 20=16+x $
 $ \Rightarrow x=4\text{ nautical miles per hour} $
Therefore, the answer to the above question is 4 nautical miles per hour.

Note: Be very careful about what is asked in the question, whether the new speed is asked or the increment in the speed is asked. Also, remember that a nautical mile is a unit of measurement used at sea distance or sea water, i.e., 1 nautical mile = 1852 meters. It is prescribed to report the answers in the same unit as the elements in the question are given, so don’t convert the distance and speed to meters.