WEIGHTED AVERAGE
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?
http://www.indo.com/cgi-bin/dist?place1=New+York%2C+NY&place2=Southampton%2C+UK
let the time taken for the ship be t hours
then the time taken by the plane is t-104 hours
so 605(t-104) = 33t
solve for t, then evaluate 33t
To find the distance between the two cities, we can use the concept of weighted average.
Let's assume the distance between New York and Southampton England is "D" miles.
The ship travels at a speed of 33 mph, so the ship's travel time is D/33 hours.
The plane travels at a speed of 605 mph and takes 104 hours less time than the ship, so the plane's travel time is D/605 hours.
We can set up the following equation based on the concept of weighted average:
D/33 = D/605 + 104
To solve this equation, we can start by multiplying all terms by the common denominator, which is (33 * 605). This will help us eliminate the denominators:
(33 * 605) * (D/33) = (33 * 605) * (D/605 + 104)
After simplifying, the equation becomes:
605D = 33D + (33 * 605 * 104)
Now, let's combine like terms:
605D - 33D = 33 * 605 * 104
572D = 33 * 605 * 104
Finally, let's solve for D by dividing both sides of the equation by 572:
D = (33 * 605 * 104) / 572
D = 186,660 miles
Therefore, the distance between New York and Southampton England is 186,660 miles.