A motorboatcan go 8 miles downstream on a river in 20 minutes. It takes 30 minutes for the boat to go upstream the same 8 miles. Find the speed of the cutrent.
Let m = speed of motorboat and c = speed of current . When going downstream, current speed is added to boat speed -- and, the total speed is "8 miles downstream in 20 minutes" . To convert to "miles per hour" we multiply by 60 mins per 1 hour: (8 miles/20 mins) * (60 mins/1 hour) = 24 mph . This gives us our first equation (1): m+c = 24 .
When going upstream, the boat speed is reduced by the current -- and, the total speed is "8 miles in 30 minutes". To convert to "miles per hour" we multiply by 60 mins per 1 hour: (8 miles/30 mins) * (60 mins/1 hour) = 16 mph . This gives us our second equation (2): m-c = 16 m = 16+c . Plug the above into equation 1 and solve for c: m+c = 24 16+c+c = 24 16+2c = 24 2c = 8 c = 4 mph
