SOLUTION: Pauline and Pete agree to meet in Columbia. Pauline travels 120 miles, while Pete travels 80 miles. If Pauline's speed is 20 miles per hour greater than Pete's and they both spend

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Question 1191071: Pauline and Pete agree to meet in Columbia. Pauline travels 120 miles, while Pete travels 80 miles. If Pauline's speed is 20 miles per hour greater than Pete's and they both spend the same amount of time traveling, at what speed does each travel?
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39629) About Me  (Show Source):
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                      SPEEDS       TIME              DISTANCE
Pauline                r+20        120/(r+20)            120
Pete                   r           80/r                   80

Given, they each travel for the same amount of time.
120%2F%28r%2B20%29=80%2Fr------simplify and solve.

Answer by ikleyn(52873) About Me  (Show Source):
You can put this solution on YOUR website!
.
Pauline and Pete agree to meet in Columbia. Pauline travels 120 miles, while Pete travels 80 miles.
If Pauline's speed is 20 miles per hour greater than Pete's and they both spend
the same amount of time traveling, at what speed does each travel?
~~~~~~~~~~~~~~~~~~


            This problem can be solved  MENTALLY,  without using equation,
            by applying reasoning and common sense. 


Since they spent the same amount of time traveling, the ratio of their rates is the same 
to the ratio of the distances.


So, the ratio of their rates is  Pauline%2FPete = 120%2F80 = 3%2F2.


Thus we can write  Pauline's rate = 3x;  Pete's rate = 2x, where x is the common measure of their rates.


Next, from the problem  3x - 2x = 20 mph,  which jives  x = 20 mph.


ANSWER.  Pauline's rate is 3*20 = 60 mph;  Pete's rate is 2*20 = 40 mph.

Solved     //     mentally.



Answer by greenestamps(13208) About Me  (Show Source):
You can put this solution on YOUR website!


Even if a formal algebraic solution is required, a solution using logical reasoning as shown by tutor @ikleyn can give you valuable mental exercise.

Here is another such solution.

The difference between the distances they traveled was 120-80=40 miles, and the difference in their speeds was 20 mph; that means the time they each traveled was 40/20 = 2 hours.

Then, since Pauline traveled 120 miles in those 2 hours, her speed was 60 mph; and since Pete traveled 80 miles in those 2 hours, his speed was 40 mph.