math

A tugboat goes upstream 120 miles in 20 hours. The return trip downstream takes 10 hours. Find the speed of the tugboat without the current and the speed of the current.

  1. 👍 0
  2. 👎 0
  3. 👁 135
  1. Set-up:
    Let v=speed of boat
    c=speed of current
    Distance = speed*time
    Upstream:
    120=(v-c)*20 ...(1)
    Downstream:
    120=(v+c)*10 ...(2)

    Solve for v and c.

    1. 👍 0
    2. 👎 0
  2. Okay, I got:
    v+6-c and c=c-6 for 120=(v-c)*20

    AND:

    c=12-v and v=6/5-c for 120=(v+c)*10

    Now what do I do?

    1. 👍 0
    2. 👎 0
  3. What you really want to do is to reduce the variables in simpler terms by dividing both sides by 20:

    v-c=120/20=6 ...(1a)
    v+c=120/10=12...(1b)

    This is a sum and difference form where the solution can be done mentally:
    v=(sum+difference)/2=9
    c=(sum-difference)/2=3

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    1.A tour boat on a river traveled 40 miles downstream in 4 hours. The return trip against the current took 5 hours. What was the rate of the current? A. 2.0 MPH B. 1.5 MPH C. 0.5 MPH D. 1.0 MPH This is also another question I did

    asked by Tia on February 3, 2015
  2. College Algebra

    Cassius drives his boat upstream for 30 minutes. It takes him 15 minutes to return downstream. His speed going upstream is two miles per hour slower than his speed going down stream. Find his upstream and downstream speed.

    asked by Lauren on September 3, 2017
  3. Math

    A tour boat on a river traveled 40 miles downstream in 4 hours. The return trip against the current took 5 hours. What was the rate of the current? A. 2.0 MPH B. 1.5 MPH

    asked by Tia on February 3, 2015
  4. algebra

    An airplane takes off from an airport and takes 6.5 hours to fly west (against the wind current) 2600 miles. The return trip (with the wind current) takes 5.2 hours. Find the airspeed and the wind speed.

    asked by McKenzie on February 27, 2014
  5. algebra

    A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the

    asked by marc on February 13, 2017
  1. Math- Multi-step word problems

    A plane traveling from Chicago to Boston with a tailwind of 10 miles per hour takes 4 hours. The return trip in the same wind, which is now a headwind, takes the same plane 4 hours and 9 minutes. According to this problem, about

    asked by Kitty on October 1, 2014
  2. how do i set up this problem?

    A cruise boat travels 48 miles downstream in 3 hours and returns upstream in 6 hours. Find the rate of the stream

    asked by Angela G on March 8, 2009
  3. 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

    asked by Ann on February 23, 2015
  4. algebra 1

    a bout travels 280 miles downstream and back. The trip downstream took seven hours. The trip back took 14 hours. The speed of the boat in still water and the speed of the current

    asked by Natalie on January 13, 2016
  5. math

    a boat travels 10 miles upstream in 4 hours. the boat travels the same distance downstream in 2 hours. Determine the rate of boat in still water and the rate of the current? Downstream speed = b(still water) + c(current) Upstream

    asked by suuny on November 20, 2016
  6. algebra

    A motorvoat goes 36 miles upstream on a river whose current is running at 3 miles per hour. The trip up and back takes 5 hours. What is the speed of the boat ( assuming that it maintains a constant speed relative to the water)?

    asked by jjj on April 4, 2011

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