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In his​ motorboat, Bill Ruhberg travels upstream at top speed to his favorite fishing​ spot, a distance of 24 ​mi, in 2 hr.​ Returning, he finds that the trip​ downstream, still at top​ speed, takes only 1.5 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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Answer:

Rate of​ Bill's boat = 14 miles per hour

Speed of the current = 2 miles per hour

Step-by-step explanation:

Let x​ = the rate of the boat in still water and y​ = the rate of the current.

Distance traveled = 24 miles

Time taken for upstream motion = 2 hour

Time taken for downstream motion = 1.5 hour

Velocity of upstream motion = x - y

Velocity of downstream motion = x + y

We have

           Displacement = Time x Velocity

Upstream motion

            24 = 2(x-y)

             x - y = 12 ----------------------------eqn 1

Downstream motion

            24 = 1.5(x+y)

             x + y = 16 ----------------------------eqn 2

eqn 1 + eqn 2

             2 x = 28

                x = 14 miles per hour

Substituting in eqn 2

                 14 + y = 16

                      y = 2 miles per hour

Rate of​ Bill's boat = 14 miles per hour

Speed of the current = 2 miles per hour

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