Going to parents house in 45 hours Travel by car 60 mph to d

Going to parent\'s house in 4.5 hours. Travel by car (60 mph) to dock where I\'ll enter a boat (20 mph on still water with 4 mph current...against me on the way to parent\'s house...with me on the way back). Takes 3.5 hours to get back home. What\'s the distance?

Solution

Let t = his time at 60 mph
:
Then (4.5 - t) = boat time at 16 mph
And (3.5 - t) = boat time at 24 mph
:
We know the trip there and the trip back are equal in distance; dist = speed*time:
60t + 16(4.5-t) = 60t + 24(3.5-t)
:
Subtract 60t from both sides, and multiply what\'s inside the brackets:
72 - 16t = 84 - 24t
-16t + 24t = 84 - 72
8t = 12
t = 12/8
t = 1.5 hrs at 60 mph
:
Total distance would be:
1.5(60) + 16(4.5-1.5) =
90 + 16(3) =
90 + 48 = 138 miles