SOLUTION: if you are rowing a boat at 40 miles an hour for 4 hours down stream and then 40 miles per hour back up stream for 10 hours what is the current

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: if you are rowing a boat at 40 miles an hour for 4 hours down stream and then 40 miles per hour back up stream for 10 hours what is the current      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 286064: if you are rowing a boat at 40 miles an hour for 4 hours down stream and then 40 miles per hour back up stream for 10 hours what is the current
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula:
d+=+r%2At where: d = distance, r = rate(speed), and t = time of travel.
In this problem, the distance, d, is the same for the downstream trip and the upstream trip, so...
For the downstream trip, the speed of the boat relative to the shore equals the boat speed on the water plus the speed of the current, so we'll let r = the boat speed and S = the speed of the current.
d%5Bd%5D+=+%28r%2BS%29%2At Substitute r = 40 mph and t = 4 hrs.
d%5Bd%5D+=+%2840%2BS%29%2A4 Simplify.
d%5Bd%5D+=+160%2B4S
For the upstream trip, let r = the boat speed and S = the speed of the current.
d%5Bu%5D+=+%28r-S%29%2At
d%5Bu%5D+=+%2840-S%29%2A10 Simplify.
d%5Bu%5D+=+400-10S But the distances are equal, so...
d%5Bd%5D+=+d%5Bu%5D then...
160%2B4S+=+400-10S Add 10S to both sides.
160%2B14S+=+400 Subtract 160 from both sides.
14S+=+240 Divide both sides by 14.
S+=+17.146
The speed of the current is 17.146 mph.