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julsineya [31]
2 years ago
6

In his​ motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing​ spot, a distance of 264 ​mi, in 6 hr.​ Re

turning, he finds that the trip​ downstream, still at top​ speed, takes only 5.5 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.
Mathematics
1 answer:
Kobotan [32]2 years ago
5 0

Answer:

The values are   x =  46 miles /hr

                            y = 4 \  miles / hr

Step-by-step explanation:

From the question we are told that

   The distance covered is  d =  264 miles

     The time taken is t_1 =  6 hours

     The time taken for the return trip is  t_2  =  5.5 \ hours

Generally during the trip  toward fishing spot , the velocity is mathematically represented as

     v_t  =  \frac{d}{t_1 } = x - y

=>  v_t  =  \frac{264}{6 } = x - y

=>    x - y  = 44 \cdots 1

Generally during the  return trip  , the velocity is mathematically represented as

      v_r  =  \frac{d}{t_2}  =  x+ y

=>   v_r  =  \frac{264}{5.5}  =  x+ y

=>   48 =  x+ y\cdots 2

add equation 1 and 2

       2x =  92

=>    x =  46 miles /hr

substituting this  into  equation 1

     46 - y  = 44 \cdots 1

=>   y = 4 \  miles / hr

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