A ship travels from New York to southampton, england at 33 miles per hour. A plane traveling 605 miles per hour takes 104 hours less time to make the same trip. How far apart are the two cities?
let the distance between the cities be d miles
time for plane = d/605
time for ship = d/33
solve for d
d/33 - d/605 = 104
( I got d = 3630)
To find the distance between New York and Southampton, we need to use the formula:
Distance = Speed × Time
Let's assume the distance between the two cities is "D" miles.
For the ship:
Distance = 33 miles/hour × Time (in hours) ----(1)
For the plane:
Distance = 605 miles/hour × (Time - 104) (since the plane takes 104 hours less time) ----(2)
Since both distances are equal (the ship and the plane cover the same distance), we can set equation (1) equal to equation (2):
33T = 605(T - 104)
Now we can solve this equation to find the value of T (Time):
33T = 605T - 61660
605T - 33T = 61660
572T = 61660
T = 61660 / 572
T ≈ 107.83 hours
Now that we have the value of T, we can substitute it back into equation (1) to find the distance between the two cities:
Distance = 33 miles/hour × 107.83 hours
Distance ≈ 3555.39 miles
Therefore, the two cities, New York and Southampton, England, are approximately 3555.39 miles apart.