Question

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.

Answer 1

The rate of the boat in still water is 44 mph and the rate of the current is 4 mph

Step-by-step 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

`(120)/(3)=x-y\\\Rightarrow 40=x-y`

Speed downstream

`(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 44 mph and the rate of the current is 4 mph