Distance = Rate * Time Problem?

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?

Answer 1

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

Answer 2

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

Answer 3

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.

Answer 4

This issue calls for the formulation d=rt, the place d is distance, r is fee or velocity, and t is time. destroy it down into 2 equations, one for uphill and one for downhill. yet, remember that she went a similar distance uphill that she did going downhill, so d=d for each leg of the run. So we could say the uphill d (it is actual a million/2 the finished distance) is fee, 2mph, circumstances time, which we are going to call t. So for the uphill a million/2, d=2t. Now for the downhill, she travelled a similar distance as she did going uphill, so because it is likewise d. She ran downhill at a fee of 3mph, and the time it took her exchange into the finished, 3, minus the time it took her to bypass uphill, which exchange into t; so the downhill equation is d=3(3-t) So the gap going uphill is represented by 2t (d=rt) the gap going downhill is represented by 3(3-t) (d=rt) We reported that the gap uphill, d, exchange into equivalent to the gap downhill, d, so then 2t would desire to equivalent 3(3-t): 2t=3(3-t) distribute 2t= 9-3t upload 3t to the two aspects 5t=9 divide the two aspects by 5: t=9/5 Now, use that interior the equations: d=2t, d=2(9/5) d=18/5 or 3 and 3/5 miles Now the different equation: d=3(3-t) d=3(3-9/5) subtract, 3=15/5 d=3(6/5) multiply d=18/5 or 3 and 3/5 miles. Now she went uphill 3 and 3/5 miles and then went downhill 3 and 3/5 miles; remember that we broke it up into halves, one a million/2 going up and one a million/2 happening, so multiply 3 3/5 *2: 18/5*2=36/5 simplify 7 a million/5 so the finished distance exchange into 7 a million/5 miles.

Answer 5

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.

Answer 6

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

Answer 7

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