SOLUTION: Two people leave from two towns that are 195 miles apart at the same time and travel along the same road toward each other. The first person drives 5 miles slower than the second

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Question 1141846: Two people leave from two towns that are 195 miles apart at the same time
and travel along the same road toward each other. The first person drives 5
miles slower than the second person. If they meet in 3 hours, at what rate
of speed did each travel?
Found 3 solutions by ikleyn, josgarithmetic, Edwin McCravy:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
If x is the rate of the slower driver (in miles per hour), then the rate of the faster driver is (x+5) miles per hour.


Then you have this "total distance" equation


    3x + 3*(x+5) = 195 miles.


This equation reflects the fact, that when they meet each other, the sum of partial distances is equal to the total distance.


From the equation,


    3x + 3x + 15 = 195

    6x = 195 - 15 

    6x = 180   =====>   x = 180/6 = 30.


ANSWER.  The slower's driver rate is 30 mph;  that of the faster driver is  30+5 = 35 mph.


CHECK.  3*30 + 3*35 = 195 miles.   ! Correct !

Solved.

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Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Speeds x and x-5

3x%2B3x-15=195
6x=195%2B15
6x=210
x=%282%2A5%2A3%2A7%29%2F%282%2A3%29
x=35

Their speeds, 35 and 30 mph

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
An alternate way to work such problems is to use rate of approach when two
things are approaching each other, or rate of separation if they are separating.

Let r = the rate of the second person.
The first person drives 5 miles slower than the second person.

So the rate of the first person is r-5.

Their approach rate is the sum of their rates or r+r-5 or 2r-5 miles per hour.
If they meet in 3 hours,

Distance = Rate × Time
     195 = (2r-5)×(3)
     195 = 3(2r-5)
     195 = 6r-15
     210 = 6r
      35 = r

So the faster one went r=35 mph and the slower one went r-5=30 mph.

Checking:  The faster one went 35 mph for 3 hours and so went 105 miles.
The slower one went 30 mph for 3 hours and so went 90 miles. And sure
enough the total distance they covered was 105+90 = 195 miles.

Edwin