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katen-ka-za [31]
3 years ago
14

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.
Physics
1 answer:
photoshop1234 [79]3 years ago
8 0

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

\frac{120}{3}=x-y\\\Rightarrow 40=x-y

Speed downstream

\frac{120}{2.5}=x+y\\\Rightarrow 48=x+y

Adding both the equations

48+40=x-y+x+y\\\Rightarrow 88=2x\\\Rightarrow 44=x

40=44-y\\\Rightarrow 40-44=-y\\\Rightarrow y=4

The rate of the boat in still water is <u>44 mph</u> and the rate of the current is <u>4 mph</u>

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