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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.

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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<h2>a) </h2>

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