Question 895456: As an aircraft carrier left hawaii traveling west seven hours before a container ship. The container ship traveled in the opposite direction going 5km/h slower then the aircraft carrier for six hours after which time the ships were 540km apart. Find the solution.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i believe you do not have enough information to get 1 solution to this problem.
you will get many.
the aircraft carrier will have traveled 13 hours.
that's 7 hours before the container ship started plus 6 hours after the container ship started.
the container ship traveled for 6 hours.
at the end of that time they were 540 km apart.
since we don't know how far apart they were when they started, we'll assign the letter d to that.
we don't also know the rate of the ships, but we do know that the container ship traveled 5 km less per hour than the aircraft carrier.
we'll assign r for rhe rate that the aircraft carrier traveled and we'll assign r-5 for the rate that the container ship traveled.
we'll assign x for the total distance that the aircraft carrier traveled.
we'll assign d - x - 540 for the total distance that the container ship traveled.
the formula for the aircraft carrier becomes x = 13r
the formula for the container ship becomes d - x - 540 = 6(r-5)
we can solve both of these equations for r to get:
r = x/13 for the aircraft carrier.
r = (d - x - 510) / 6
we can set these equations equal to each other to get:
x/13 = (d - x - 510) / 6
we can solve this equation for x to get:
x = (13d - 6630) / 19
we need to know the value of d to get an exact answer.
as this equation stands, x will be different values depending on the different value of d.
let's assume that d = 1000 km.
solve for x to get x = 335.2631...
that means that 1000 - x - 540 = 124.73684...
335.2631... is the distance that the aircraft carrier traveled.
124.73684... is the distance that the container ship traveled.
solve for their rates and you get the rate of the aircraft carrier is equal to 25.78947... km per hour and the ratge of the container ship is equal to 20.78947... km per hour, the difference being 5 km per hour.
assume a different value for d and you get a different value for x and a different value for d - x - 540 and you subsequently get a different rate for the aircraft carrier and a different rate for the container ship, but the difference in their rates will still be 5 km per hour.
for example, when d = 25000, x = 16756.31579 km and d - x - 540 = 7703.6842...
solve for their rates and you get the rate of the aircraft carrier is equal to 1288.947368... km per hour and the rate of the container ship is equal to 1283.947368... km per hour.
not very realistic, but the rates are still 5 km difference from each other.
bottom line is that you will get an infinite number of answers depending on the value of d which was not given.
d is the total distance between the ships when they both started.
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