Question

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

Answer 1

The values are
`x =  46 miles /hr`

`y = 4 \  miles / hr`

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  =  (d)/(t_1 ) = x - y`

=>
`v_t  =  (264)/(6 ) = x - y`

=>
`x - y  = 44 \cdots 1`

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

`v_r  =  (d)/(t_2)  =  x+ y`

=>
`v_r  =  (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`