SOLUTION: A freighter leaves port steaming South. Two hours later a Coast Guard Cutter located 50 miles to the north of the port is ordered to give chase. If it takes the cutter 4 hours to o

Question 4290: A freighter leaves port steaming South. Two hours later a Coast Guard Cutter located 50 miles to the north of the port is ordered to give chase. If it takes the cutter 4 hours to overtake the ship steaming at 20 miles per hour faster, how fast were both traveling?
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Let x = rate of the freighter.
x + 20 = rate of the Coast Guard Cutter
4 + 2 = 6 = time of the freighter
4 = time of the Coast Guard Cutter

D=RT
6x= distance of the freighter
4(x + 20) = distance of Coast Guard Cutter

The equation is based upon the fact that:

Distance traveled by the Coast Guard Cutter is 50 miles more than the distance traveled by the freighter
4(x + 20) = 6x + 50
4x + 80 = 6x + 50

Subtract 4x from each side:
4x - 4x + 80 = 6x - 4x + 50
80 = 2x + 50

Subtract 50 from each side:
80 - 50 = 2x + 50 - 50
30 = 2x
x = 15 mph = rate of the freighter
x+20 = 35 mph = rate of Coast Guard Cutter.

Check: Freighter travels 15 mph for 6 hours, which is 90 miles. The Coast Guard Cutter travels at 35 mph for 4 hours, which is 140 miles, a difference of 50 miles.

Nice problem.

R^2 from SCC

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