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Find the rate of the rowers in calm water and the rate of the current

A row boat team travelled with the current 36 miles in 2 hours. Coming back against the current, it took 3 hours to cover the same distance. Find the rate of the rowers in calm water and the rate of the current.

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Brad M. | Summer Online Finance Specialist: WACC NPV DCF TVM YTMSummer Online Finance Specialist: WACC ...
4.9 4.9 (233 lesson ratings) (233)
Hey Donald -- a "verbal" reasoning approach ... 18mph downstream, 12mph upstream ...
the midpoint is 15mph for rowers, with +/- 3mph on each side for the current ... Best :)
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
Hi Donald;
with the current...(36 miles)/(2 hours)=(18 miles)/hour
against the current...(36 miles)/(3 hours)=(12 miles)/hour
x=rate in calm waters
with the current...x+y=(18 miles)/hour
against the current...x-y=(12 miles)/hour
Let's subtract the two equations from each other...
(x-x)+y-(-y)=(6 miles)/hour
0+y+y=(6 miles)/hour
2y=(6 miles)/hour
y=3 miles/hour
Let's add the two equations together...
(x+x)+(y-y)=(30 miles)/hour
2x+0=(30 miles)/hour
2x=(30 miles)/hour
x=(15 miles)/hour
Let's check our work...
with the current...
[(15 miles)/hour]+[(3 miles)/hour)]=(18 miles)/hour
against the current...
[(15 miles)/hour]-[(3 miles)/hour)]=(12 miles)/hour
Tom D. | Very patient Math Expert who likes to teachVery patient Math Expert who likes to te...
One must presume that the 'rate of the rowers' is the same both ways
Rr: Rate of rowers
Rs: Rate of stream
Td: Time downstream
Tu: Time upstream
1: (Rr+Rs) = D/Td = 18 mi/hr
2: (Rr - Rs) = D/Tu = 12 mi/hr
Adding the two equations (1 & 2)yields
2Rr = 30 mi/hr
Rr = 15 mi/hr
Substituting Rr back into 1)
Rs = 3 mi/hr