# Help with a word problem?

A boat goes 48 miles downstream with the current in 3 hours and returns upstream against the current in 4 hours. Find the rate of the boat in still water and rate of the current flow.

Please show work so I can understand. Thanks!

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• Anonymous
8 years ago

b = boat speed

c = current speed

b + c = 48mi/3hr = 16mi/hr

b - c = 48mi/4hr = 12mi/hr Solve this one for b and substitute that into the first equation.

b = 12 + c

12 + c + c = 16

2c = 4

c = 2 mi/hr Plug this value into either equation and solve for b.

b + 2 = 16

b = 14 mi/hr

• A boat goes 48 miles downstream with the current in 3 hours and returns against the

current in 4 hours. Find the rate of the boat in still water and rate of the current flow.

S = D/T

S = speed in mph

D = distance in miles

T = time in hours

Downstream

Sd = 48 mi/3 hr = 16 mph

D = ST

D = 16(3) = 48

(Sb + Sc) = 16

Sc = 16 - Sb

Upstream

Su = 48 mi/4 hr = 12 mph

D = ST

D = 12(4) = 48

(Sb - Sc) = 12

Sb = 12 + Sc

Sb -12 = Sc

Sc = Sb - 12

16 - Sb = Sb - 12

16 = 2Sb - 12

16 + 12 = 2Sb

28 = 2Sb

2Sb = 28

Sb = 28/2 = 14 mph Speed of boat in still water

Downstream

Sc = 16 - Sb

Sc = 16 - 14 = 2 mph Speed of current

Upstream

Sc = Sb - 12

Sc = 14 - 12 = 2 mph Speed of current

• b + c = 16 mi/hr

b - c = 12 mi/hr

2b = 28 mi/hr

b = 28/2 = 14 mi/hr <<rate of the boat in still water

using the first equation:

14 + c = 16

c = 16 - 14 = 2 mi/hr <<rate of current flow

check using the second equation:

14 - 2 = 12

12 = 12

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