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On a particular day, the wind added 4 miles per hour to Jaime's rate when she was rowing with the wind and subtracted 4 miles per hour from her rate on her return trip. Jaime found that in the same amount of time she could row 57 miles with the wind, she could go only 33 miles against the wind.What is her normal rowing speed with no wind?

Respuesta :

qeven1
24 is her normal rowing speed

Answer:

15 mph

Step-by-step explanation:

Speed of wind = [tex]V_w[/tex] = 4 mph

Speed of Jaime rowing = [tex]V_r[/tex]

Speed of boat against wind = [tex]V_r-4[/tex].

Speed of boat with wind = [tex]V_r+4[/tex]

Time taken with and against wind is same = t

Distance travelled with wind = 57 mph

Distance travelled against wind = 33 mph

[tex]time=\frac{\text{Distance}}{\text{Speed}}[/tex]

Time taken to go with wind

[tex]t=\frac{57}{V_r+4}[/tex]

Time taken to go against wind

[tex]t=\frac{33}{V_r-4}[/tex]

So,

[tex]t=\frac{57}{V_r+4}=\frac{33}{V_r-4}\\\Rightarrow \frac{57}{33}=\frac{V_r+4}{V_r-4}\\\Rightarrow 57V_r-33V_r-228-132=0\\\Rightarrow V_r=\frac{360}{24}\\\Rightarrow V_r=15\ mph[/tex]

∴ Her normal rowing speed with no wind is 15 mph

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