SOLUTION: to deliver a package a messenger must travel at a speed of 60mi/h on land and then use a motor boat who's speed is 20 mi/h in still water. The messenger goes by land to a dock and

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Question 252981: to deliver a package a messenger must travel at a speed of 60mi/h on land and then use a motor boat who's speed is 20 mi/h in still water. The messenger goes by land to a dock and then travels on a river against a current of 4 mi/h . He reaches the destination in 4.5 hours and then returns to the starting point in 3.5 hours. How far did the messenger travel by land and how far by water.
Please help with step by step instructions for problem solving.. THANKS...
Answer by Greenfinch(383) (Show Source):
You can put this solution on YOUR website!
The key to this is the river current.
Outward the boat does 16 mph and back it does 24 mph. The difference in time is 1 hour.
So D/16 = T + 1, D/24 = T
Equating distance gives 16T + 16 = 24T
8T = 16, so T = 2
So it takes 2 hours at 24 mph and 3 hours at 16 mph. The distance on the river is 48 miles. The remaining time in both cases is 1.5 hours, which is done at 60 mph and is therefore 90 miles.
Total distance is 90 land plus 48 water or 138 miles