Question 1205185: Hi
Ted and Justina took part in a race. Ted won the race 25 minutes after it started. Justina had only run 5/8 of the distance. Justinas average speed was 75 m per minute slower than Ted. What was Ted's average speed in the race
Thanks
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
x = Ted's speed
x-75 = Justina's speed
Each speed is in meters per minute.
For Ted,
distance = rate*time
distance = (x meters per min)*(25 min)
distance = 25x
Now find the distance Justina traveled in the same 25 minute time frame.
distance = rate*time
distance = (x-75)*(25)
distance = 25(x-75)
distance = 25x-1875
Ted ran 25x meters which is the full track.
Justina ran 25x-1875 meters (i.e. 1875 meters less than a full track). Her distance is 5/8 of Ted's distance.
So,
Justina's distance = (5/8)*(Ted's distance)
25x-1875 = (5/8)*(25x)
8(25x-1875) = 5(25x)
200x - 15000 = 125x
200x-125x = 15000
75x = 15000
x = 15000/75
x = 200
200 meters per minute might sound like a lot, but it converts to roughly 7.456 mph, which is a typical average running speed.
Sprinting speeds will likely exceed this, but keep in mind that we're talking about an overall average over the course of 25 minutes.
Answer by ikleyn(52775)  (Show Source):
You can put this solution on YOUR website! .
Ted and Justina took part in a race. Ted won the race 25 minutes after it started.
Justina had only run 5/8 of the distance. Justinas average speed was 75 m per minute slower than Ted.
What was Ted's average speed in the race
~~~~~~~~~~~~~~~~~~~~~
When Ted completed the race, Justina had only run 5/8 of the distance.
It means that Justina' speed was 5/8 of the Ted' speed.
Let x be the Ted' speed (the unknown value under the problem's question).
Then the Justina' speed was  .
The difference is given
x - = 75 meters per minute.
Hence,
 = 75 ---> x =  = 25*8 = 200.
ANSWER. Ted' speed was 200 meters per minute in this race.
Solved.
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Notice that Ted's time to complete the race (25 minutes, given)
is NON-NECESSARY and EXCESSIVE data in this problem.
I did not use it in my solution.
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So, this problem has excessive data.
Is it good or bad ? - - - Or neutral ?
It depends on the problem' style and on the goal of a composer.
Sometimes, it is good in joke Math problems - but this one is not of that style.
Sometimes, it is good to keep a reader in good tonus to recognize an excessive info
and to check, if it is consistent with the rest of given information.
But again, in this posted problem I do not see explicit signs of such intentions from a composer' side.
Then only last reason remains - the excessive info is a result of the composer's fault.
It definitely confuses a reader and perplexes him/her - especially a beginner student.
Without a necessity, it is strongly recommended in Math do not create such problems,
since they only diminish authority of real Math composers and a Math as a whole subject
- and destroy fragile logical system in the heads of students.
Destroy - instead of Building it and Teaching properly.
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