Question

In his​ motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing​ spot, a distance of 270 ​mi, in 5 hr.​ Returning, he finds that the trip​ downstream, still at top​ speed, takes only 4.5 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

Answer:

D = rate x time

 

D = (rate of current + rate of boat) x time

 

168 = (y - x) t against the current trip upstreams

168 = (y + x) t with the current trip downstream

 

168 = (y - x) 4

168 = (y + x) 3.5

 

since 168 = 168, we can set the equations equal to each other:

 

(y - x)4 = (y+x)3.5

4y - 4x = 3.5y +3.5x

4y - 3.5y = 3.5x + 4x

0.5y = 7.5x

y =15x

 

the rate of the current is 15 times the rate of the boat.

168 =4(15x) - 4x

168 = 60x - 4x

168 = 56x

x = 3

 

y = 15x

y = 15(3)

y = 45

 

Step-by-step explanation: