SOLUTION: Hama is training by running to a post across a field and then back. She runs the outward leg at 7 m/s and the return leg at 5 m/s. She takes 15.4 s. Find the distance to the post.

Question 766777: Hama is training by running to a post across a field and then back. She runs the outward leg at 7 m/s and the return leg at 5 m/s. She takes 15.4 s. Find the distance to the post.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Uniform Rates problem, with basic equation ;
r is meters per second, rate or "speed"
t is time in seconds
d is distance in meters

Hama traveled two equal distances each at different rate.
This data table represents the given information in columns arranged as speed, time, distance. Note that we neither know the distance to the post, but here I have given the variable, d.

To Post___________7________(__)_______(d)
Back from Post____5________(__)_______(d)
Total_______________________15.4__________

Use the basic equation to find expressions for the missing times.
_______________speed_______time_______distance
To Post___________7________(d/7)_______(d)
Back from Post____5________(d/5)_______(d)
Total_______________________15.4__________

We can form an equation for the total time to run to the post and back.

The rest of the process is simple arithmetic.
---Distributive Property used in reverse
---combined step, fractions to higher terms using LCD and adding
----multiply members by multiplicative inverse
meters

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NOTE: Explanations for steps included now.
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