Abhishek is planning a journy by ship to Andaman. Andaman trip in itself is an adventure. There are three ports in India from where you can sail to Andaman; Kolkata, Chennai, and Vishakhapatnam. Abhishek did not know the length of journey so he took the help of an expert who helped him by solving a sample mathematical situation related to ships.
The ship covered a certain distance at a uniform speed of ship would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And if the speed of ship were slower by 6km/h, it would have taken 6 hours more than the scheduled time. Find the length of the journey.
Answers
The answer is 720 km
GIVEN
The ship covered a certain distance at a uniform speed of ship would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And if the speed of ship were slower by 6km/h, it would have taken 6 hours more than the scheduled time.
TO FIND
Find the length of the journey.
SOLUTION
We can simply solve the above problem as follows;
Let the actual speed of the ship = x km/hr
Actual time taken for arrival = y hours
Distance travelled = speed × time = xy km
In first case;
.Speed of the ship = (x + 6) km/hr
Time of the ship = (y-4) hour
Distance covered = (x + 6) (y-4)
xy = ((x + 6) (y-4)
-4x + 6y - 24 = 0
= -2x + 3y - 12 = 0 (Equation 1)
In second case;
Speed of the ship = (x-6)km/hr
Time of the ship = (y+ 6) hour
xy = (x-6)(y+6)
= 6x - 6y = 36
= x - y -6 = 0 (Equation 2)
Cross multiplying equation 1 and 2
= x/-30 = -y/24 = 1/-1
= x = 30 km/hr
y = 24 hours
Distance covered = 30 × 24 = 720 km
Hence, The answer is 720 km
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