A ship is running at 14 3/4 knots (nautical miles per hour) for 7 1/2 hours. How far does the ship travel?
To find the distance traveled by the ship, we can use the formula:
Distance = Speed × Time
Given that the ship is running at a speed of 14 3/4 knots for 7 1/2 hours, we can substitute these values into the formula:
Distance = (14 3/4) knots × 7 1/2 hours
To simplify the calculation, we convert the mixed numbers to improper fractions:
14 3/4 = (4 × 14 + 3) / 4 = 59/4
7 1/2 = (2 × 7 + 1) / 2 = 15/2
Let's substitute these values into the formula and calculate the distance:
Distance = (59/4) knots × (15/2) hours
To multiply fractions, we multiply the numerators together and the denominators together:
Distance = (59 × 15) / (4 × 2)
Multiplying the numerators and denominators:
Distance = 885 / 8
To express the result as a mixed number, we divide the numerator by the denominator:
885 ÷ 8 = 110 remainder 5
Therefore, the distance traveled by the ship is 110 5/8 nautical miles.
To find how far the ship travels, we need to multiply the speed of the ship by the time it is traveling.
First, let's convert the speed of the ship from knots to nautical miles per hour. Since 1 knot is equal to 1 nautical mile per hour, we can keep the speed as it is.
The speed of the ship is 14 3/4 knots, which can be written as a mixed number (14 + 3/4).
Next, we multiply the speed by the time to get the distance traveled.
Distance = Speed * Time
Speed = 14 3/4 knots = 14.75 knots
Time = 7 1/2 hours = 7.5 hours
Distance = 14.75 knots * 7.5 hours
Now we can simply multiply the speed and time to get the distance traveled.
Distance = 110.625 nautical miles
Therefore, the ship travels approximately 110.625 nautical miles.