Question 1123268: The cost of running a ship at a constant seed of v km/h is 160 +1/100 * v^3 dollars per hour.
a) Find the cost of a journey of 1000km at a speed of 10km/h.
b) Find the cost, C dollars, of a journey of 1000km at a speed of v km/ h
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! part a:
at 10 kmph, the total cost would be 160 + (1/100 * 10^3 dollars per hour * the number of hours).
that makes it 160 + (10 dollars per hour * the number of hours)
a 1000 km journey at a speed of 10 km per hour takes 100 hours.
this is based on the formula of rate * time = distance.
when rate = 10 and distance = 1000, formula becomes 10 * time = 1000
solve for time to get time = 1000 / 10 = 100 hours
the total cost is therefore 160 + (10 dollars per hour * 100 hours) = 1,160 dollars.
the 160 is the up front cost for the trip.
1/100 * v^3 is the variable cost per hour.
this depends on the speed of the boat.
multiply that by the hours and add it to the up front cost and you get the total cost for the trip.
part b:
the distance is 1000 km and the speed is v kmph.
the total cost of the journey is 160 + (1/100 * v^3 dollars per hour * the number of hours).
rate * time = distance.
rate is v kmph
distance is 1000 km
solve for time to get:
time = (1000 / v) hours
total cost of the journey becomes 160 + (1/100 * v^3 * 1000 / v)
at 10 kmph, this becomes 160 + (1/100 * 10^3 * 1000 / 10) = 1,160.
since we already did 1000 km at 10 kmph in part a, i used that again to confirm the formula is good at v kmph by setting v = 10 kmph.
the formula looks good.
your solution for part a is 1,160 dollars for the total cost of the journey at 10 kmph.
your solution for part b is 160 + (1/100 * v^3 * 1000 / v) dollars for the total cost of the journey at v kmph.
|
|
|
