Another word problem

mkay

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A runner decides to run out in the country. He begins to run at an average rate of 9mph. He runs a certain distance and then turns around and returns along the same route at an average rate of 6mph. If the round trip took 2 and a half hours, how far did the runner travel before turning around? Every other distance/rate/time problem I've looked at hasn't helped me figure this one out. thanks
 
A runner decides to run out in the country. He begins to run at an average rate of 9mph. He runs a certain distance and then turns around and returns along the same route at an average rate of 6mph. If the round trip took 2 and a half hours, how far did the runner travel before turning around? Every other distance/rate/time problem I've looked at hasn't helped me figure this one out. thanks

1. Use the definition of speed:

speed=distancetime      distance=speedtime\displaystyle \displaystyle{speed = \frac{distance}{time}~\implies~distance = speed \cdot time}

2. Let t1\displaystyle t_1 denotes the time for the 1st part of the run and t2\displaystyle t_2 the time for the 2nd part. Then you know:

t1+t2=529t1=6t2\displaystyle \left|\begin{array}{rcl}t_1+t_2&=&\frac52 \\ 9t_1&=& 6t_2\end{array}\right.

3. Solve for t1\displaystyle t_1 and t2\displaystyle t_2 and consequently determine the corresponding distances.
 
Last edited:
Hello, mkay!

A runner decides to run out in the country.
He begins to run at an average rate of 9mph.
He runs a certain distance and then turns around
. . and returns along the same route at an average rate of 6mph.
If the round trip took 2 and a half hours,
. . how far did the runner travel before turning around?

Formula: Time=DistanceSpeed\displaystyle \text{Formula: } \:\text{Time} \:=\:\dfrac{\text{Distance}}{\text{Speed}}

Let x\displaystyle x = distance (one way).

He ran x\displaystyle x miles at 9 mph.
. . This took x9\displaystyle \dfrac{x}{9} hours.

He ran x\displaystyle x miles at 6 mph.
. . This took x6\displaystyle \dfrac{x}{6} hours.

His total time was 212\displaystyle 2\frac{1}{2} hours.
There is our equation! . \(\displaystyle \hdots \;\;\dfrac{x}{9} + \dfrac{x}{6} \:=\:\dfrac{5}{2}\)

Go for it!
 
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