Question 80830: Two vagabonds who are 200 miles apart travel towards each other. If they start at 2 p.m. and meet at 6 p.m., and one vagabond is traveling 10 miles per hour faster than the other, what are the speeds of both vagabonds?
I tried using rate x time = distance like our teacher said, and this is what i got::
((Vagabond A, Vagabond B))
..........(r)........(t)..=..d
A........x
B........x+10
total................4h.....200mi
Then i divided 200 by 4 and got 50, so I got 50 mph and 60 mph... am I right?
Thank You!
Jamie
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let's check your answer. One vagabond is going at a rate of 50 miles per hour. The time
at this rate is 4 hours (2 pm to 6 pm). In that 4 hour period at 50 miles per hour, that
vagabond travels the full 200 miles by itself. If that doesn't seem right, it means that
your answer is incorrect because the second vagabond wasn't even taken into consideration.
.
Here's the way to do the problem.
.
Use the distance formula for the vagabond that travels at the unknown rate R. When you do you
get that the distance (D1) for the first vagabond is:
.
D1 = R*T
.
At this point we know that T is 4 hours. So we can substitute 4 for T and the equation
then becomes:
.
D1 = R*4 = 4R
.
Now let's do the same thing for the second vagabond. It has a rate equal to the rate of
the first vagabond plus 10 miles per hour, so its rate is R+10. It also travels for 4 hours.
If the distance traveled by this second vagabond is D2 then its distance equation is:
.
D2 = (R+10)*4
.
Multiply out the right side and you get:
.
D2 = 4R + 40
.
Now recognize that when the two vagabonds meet, the total distance (D1 + D2) that they
travel is 200 miles. So lets add our two distance equations:
.
D1 = 4R
D2 = 4R + 40
.
When you add these vertically you get:
.
D1 + D2 = 8R + 40
.
But we already noted that D1 + D2 is 200 miles. So we can substitute 200 for D1 + D2 and
we get:
.
200 = 8R + 40
.
Get rid of the 40 on the right side by subtracting 40 from both sides. When you do that the
equation becomes:
.
160 = 8R
.
Finally, solve for R by dividing both sides by 8 and you get:
.
R = 160/8 = 20 miles per hour
.
So the rate of the first vagabond is 20 miles per hour and the rate of the second vagabond
is 10 miles per hour faster or 30 miles per hour.
.
Let's check these answers.
.
At 20 miles per hour, in 4 hours the first vagabond goes 80 miles toward the second vagabond.
.
Meanwhile at 30 miles per hour, in 4 hours the second vagabond goes 120 miles toward the
first vagabond.
.
This combination means that in the 4 hours the two together cover 80 + 120 miles and when
that is done they meet having covered the 200 miles between them when they started out.
.
Hope this helps you to understand the problem and how your teacher said you could use
the distance formula to solve it.
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