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A professional rower can paddle 320 miles upstream in 10 hours and downstream 320 miles in 5 hours. How fast is the current? (don't forget your units)

 Jan 21, 2020
 #1
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Let  R  =  rate of the rower in still water.

Let  S  =  rate of the stream.

 

Downstream, the final rate is R + S.

Upstream, the final rate is R - S.

 

Using the formula  Distance  =  Rate x Time:

 

Downstream:  320  =  (R + S)(5)     --->     320  =  5R + 5S     --->     x2     --->     640  =  10R + 10S

Upstream:       320  =  (R - S)(10)    --->     320  =  10R - 10S

 

Combining the equations:     640  =  10R + 10S

                                              320  =  10R - 10S

 

Adding down the columns:   960  =  20R     --->     R  =  960 / 20  =  48 mph

 

To Find S:  320  =  5R + 5S     --->     320  =  5(48) + 5S     --->     320  =  240 + 5S     --->     80  =  5S     --->     S  = 16 mph     

 Jan 21, 2020
 #2
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+1

320 / 10 = 32 mph - his speed upstream

320 / 5   = 64 mph - his speed downstream

 

[64 + 32] / 2 = 48 mph - hid speed in still water.

[64 - 32] / 2 = 16 mph - the speed of the current .

 Jan 22, 2020

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