| Distance = Rate * Time Problem?

Distance = Rate * Time Problem?

Audy asked the question:


A man has 3.25 hours in which to give some friends a tour of the surrounding countryside. How farm from the house can the tour extend if the speed on the trip out is 25km/h and the speed of the return trip is 40km/h?

This is a distance = rate*time problem and I am very bad with word problems..can someone please explain to me on how to do this step by step?

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Comments

6 Responses to “Distance = Rate * Time Problem?”

  1. James Chan on February 15th, 2009 12:45 pm

    let x be the distance they have gone from his house
    we have
    x / 25 + x / 40 = 3.25(3.25 is the total time in which they go there and return the house)
    => x = 50 km

  2. ichliebedichx on February 18th, 2009 9:00 pm

    The thing to understand first is that distance on the way out and on the way back have to equal the same number. Now, we set up two different equations for the two different rates that result in distance as the answer. For example:

    Distance = rate*time
    Let’s set distance equal to D.
    D = rate*time
    For the way out: 25km/h is the rate.
    D = 25*time
    In order to figure out time, we have to take the total time and subtract one way. We can set the way BACK as x. Thus, the way out would equal 3.25-x. We place that in the equation.
    D = 25*(3.25-x)
    There’s the first equation.

    Second, we do the same for the way back.
    D is still equal to distance because the distance out and the distance back should be the same.
    D = rate*time
    Since we already know the rate, and the time we just plug them in. The second equation looks like this:
    D=40*x

    We now combine these two equations. Since D = D and 40*x = D, as well as 25*(3.25-x) = D then the two of them equal each other. So our final equation is:

    40x = 25(3.25 - x)
    40x = 81.25 - 25x
    65x = 81.25
    x = 1.25

    Now we go back and figure out the distance. In order to do that, you just plug x into an original equation.

    For example:

    Distance = rate*time
    We have the rate…
    40 km/h
    Time is X or as we figured out 1.25
    D = 40 (1.25)
    D= 50 km

  3. Helmut on February 22nd, 2009 5:55 am

    t1 = d/25
    t2 = d/40
    tt + t2 = 3.25 hr = d(1hr/25km + 1hr/40km)
    d = (3.25)(hr/hr)(200 km)/(200 km/25 km + 200 km/40 km)
    d = 650 km/(8 + 5)
    d = 650 km/13
    d = 50km

    Check:
    t1 = 2hr
    t2 = 1.25 hr
    t1 + t2 =3.25 hr

  4. northstar on February 22nd, 2009 1:41 pm

    time = distance / rate

    Let
    d = one way distance
    r1 = rate out = 25 km/hr
    r2 = rate back = 40 km/hr
    t1 + t2 = 3.25 hours

    We have:

    t1 + t2 = d/r1 + d/r2
    3.25 = d/25 + d/40
    200*3.25 = 8d + 5d
    650 = 13d
    d = 650/13 = 50 km

    He can go 50 km out from the house.

  5. Taylor S on February 23rd, 2009 7:05 pm

    3.25*25=81.25
    3.25*40=130
    81.25+130=211.25km
    thats wat i wuld hav sed dont take ma word 4 it lol

  6. sarkartapas2005 on February 24th, 2009 10:11 pm

    The answer given by james chan is the best.let me solve it arithmatically.
    iIf the distance is 1 Km,it will take 1/25 hr. for going and 1/40 hr for returning.
    Therefore,total time =(1/25 +1/40)=13/200 hr or 0.65 hr
    Therefore the tour would extend to (3.25/0.65 or) 50 km.