Algebra

The current of a river moves at 3 miles per hour. It takes a boat 3 hours to travel 12 miles upstream, against the current, and return the same distance traveling downstream, with the current. What is the boats rate in still water?

  1. 👍
  2. 👎
  3. 👁
  1. boat's speed in still water --- x mph
    against the current ----- x-3 mph
    with the current -------- x + 3 mph

    time against current = 12/(x-3)
    time with the current = 12/(x+3)

    12/(x+3) + 12/(x-3) = 3
    times (x-3)(x+3) or x^2 - 9
    12(x-3) + 12(x+3) = 3(x^2 - 9)
    12x-36 + 12x + 36 = 3x^2 - 27
    3x^2 - 24x - 27 = 0
    x^2 - 8x - 9 = 0
    (x-9)(x+1) = 0
    x = 9 or x = -1, I guess we'll reject that negative

    the boat's speed in calm water is 9 mph

    check:
    12/12 + 12/6
    = 1 + 2
    = 3hrs.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math! Algebra 1!

    A boat is traveling in a river with a current that has a speed of 1.5 km/h. In one hour, the boat can travel twice the distance downstream as it can travel upstream. How long will it take the boat to travel 100 km in still water?

  2. phys science

    1. speed is the ratio of the distance an object moves to a. the amount of time needed to travel the distance** b. the direction the object moves c. the displacement of an object d. the motion of the object 2. a car traveled 60 km

  3. physics

    A boat travels at 3.8 m/s and heads straight across a river 240 m wide. The river flows at 1.6 m/s. Find A) The boat's resultant velocity. B) How long it takes the boat to cross the river. C) How far downstream the boat is when it

  4. math

    The Connecticut River flows at a rate of 5 km / hour for the length of a popular scenic route. If a cruiser to travels 4 hours with the current to reach a drop-off point, but the return trip against the same current took 6 hours.

  1. Pre-Cal

    A pilot wishes to fly on course 290 with an air speed of 300 knots when the wind blows from 224 at 18 knots. Find the drift angle to the nearest hundredth of a degree. A.3.22° B.5.07° C.86.86° A river is flowing at the rate of

  2. Algebra

    A boat has a speed of 20 mph in still water. While traveling on a river at top speed, it went 40 miles upstream in the same amount of time it went 60 miles downstream. Find the rate of the river current.

  3. Algebra 2

    The excursion boat on the river takes 2½ hours to make the trip to a point 12 miles upstream and to return. If the rate at which the boat travels in still water is 5 times the rate of the river current, what is the rate of the

  4. Mathematics

    1. The speed of a current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat for his business. Every day, his route takes him 22.5 miles each way against the current and back to his

  1. Intermediate Algebra Word Problem

    A river's current is 4mph. A boat travels 48 miles downstream in the same time it travels 24 miles upstream. Find the speed of the boat. A) What does the variable stand for? x stands for the speed of the boat. B) Write the

  2. Math

    A boat, which moves at 18 mph in still water, travels 14 miles downstream in the same amount of time it takes to travel 10 miles upstream. Find the speed of the current.

  3. Math

    A ferry boat departed from port and traveled at a rate of 10 miles per hour at an angle 30° north of East across a large river. If the current is flowing at a rate of 4 miles per hour straight south, what is the speed and

  4. algebra

    Show a complete solution. Upstream, downstream. Junior’s boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of

You can view more similar questions or ask a new question.