Amotor boat traveled 18 miles down a river in 2 hours but took 4.5 hours to return upstream. find the rate of the motor boat in still water and the rate of the current. (round to the nearest tenth).

rate of the boat in still water = 6.5 miles / hourrate of the current = 2.5 miles / hour.

Explanation:

1) Name the two variables:

c: rate of the currentb: rate of the boat in still water:

With that, the net rates of the boat down the river and upstrean are:

down the river: b + cupstream: b - c

2) Now set the equations for the distance as a function of the times and the rates:

distance = rate × timedownstream: 18 miles = (b + c) × 2 hoursupstream: 18 miles = (b - c) × 4.5 hours

3) Set the system of equations:

18 = 2(b + c) ⇒ 9 = b + c . .  . Equation (1)18 = 4.5 (b - c) ⇒ 4 = b - c . . . Equation (2)

4) Solve the system by elimination:

Add equations (1) and (2): 9 + 4 = 2bDivide both sides by 2: 13/2 = bSimplify: b = 6.5Replace b with 6.5 in equation (2) and solve:

       4 = 6.5 - c ⇒ c = 6.5 - 4 = 2.5

5) Results:

b = rate of the boat in still water = 6.5 miles / hourc = rate of the current = 2.5 miles / hour.