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In his​ motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing​ spot, a distance of 120120 ​mi, in 33 hr.​ Returning, he finds that the trip​ downstream, still at top​ speed, takes only 2.52.5 hr. Find the rate of​ Bill's boat and the speed of the current. Let x​ = the rate of the boat in still water and y​ = the rate of the current.

Answer :

Answer:

The rate of the boat in still water is 44 mph and the rate of the current is 4 mph

Explanation:

x​ = the rate of the boat in still water

y​ = the rate of the current.

Distance travelled = 120 mi

Time taken upstream = 3 hr

Time taken downstream = 2.5 hr

Speed = Distance / Time

Speed upstream

[tex]\frac{120}{3}=x-y\\\Rightarrow 40=x-y[/tex]

Speed downstream

[tex]\frac{120}{2.5}=x+y\\\Rightarrow 48=x+y[/tex]

Adding both the equations

[tex]48+40=x-y+x+y\\\Rightarrow 88=2x\\\Rightarrow 44=x[/tex]

[tex]40=44-y\\\Rightarrow 40-44=-y\\\Rightarrow y=4[/tex]

The rate of the boat in still water is 44 mph and the rate of the current is 4 mph

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