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.

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

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!