In his motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing spot, a distance of 90 mi, in 3 hr. Returning, he finds that the trip downstream, still at top speed, takes only 2.5 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.
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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:
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