SOLUTION: Andrea has 4 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool dow

Question 1145893: Andrea has 4 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 8mph
and walks back at a speed of 2mph, how long should she plan to spend walking back?
Found 4 solutions by ikleyn, josgarithmetic, MathTherapy, richwmiller:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

Her time walking back is 4 times her time running the distance of the race. Is it what you want to find out ?

In my view, the problem formulation is not perfectly clear; therefore, I only can make my hypotheses on what you want to know . . .

===============

My note after reading the solution bt @josgarithmetic.

It is tooooo soft from my side to say that the problem formulation is not perfectly clear. It is simply CATASTROPHICALLY BAD.

I just saw ~ 5000 times in this forum as "the students" try to create their own problems/formulations without having
any knowledge/experience/notions on how to do it . . .

I just noticed it in one of my previous comments (long time ago):

The better English is, the worst is Mathematical meaning and Educational value of such "inventions". Precise and exact illustration. Simply former English teacher tries to work as a mathematician. Clear as a day . . .

The simple rule and criterion is: a good Math problem formulation is a piece of art.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

Same distance d for running as for walking back SPEED TIME DISTANCE RUN 8 d/8 d WALK 2 d/2 d TOTAL 4

Time for walking back:

3 hours 12 minutes
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Andrea has 4 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the race and walking back the same distance to cool down. If she runs at a speed of 8mph
and walks back at a speed of 2mph, how long should she plan to spend walking back?

Let time she should plan on spending to walk back be T
Then we get the following DISTANCE equation: 2T = 8(4 - T)
2T = 32 - 8T
2T + 8T = 32
10T = 32
T, or time she should plan on spending to walk back =
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
The problem as posted is perfectly clear for people who understand English and its nuances.
The question posed is "How long should she plan to spend walking back?"
The question couldn't be clearer.
"How long" when referring to time (which is the reference here) means "How much time?"
Both tutors MathTherapy and josgarithmetic presented a good understanding of the problem and a proper approach to a solution.
A quicker and easier way to solve the problem might begin with tutor ikleyn's comment that her time walking back is 4 times her time running the distance of the race.
So we can take the 4t +t=5t
Now we take the 4 hours multiply by 4/5 to get 3.2 hours as both tutors MathTherapy and josgarithmetic found. Tutor josgarithmetic went a step further and converted .2 hr ( i.e. 1/5 hr) to 12 minutes.
So the simple solution"
8/2=4 times as fast
4t+t=5t
4.0*4/5=3.2 hours=3 hr 12 minutes to walk back
Some tutors who don't understand English should be careful about complaining about perfectly clear problems. Sometimes, their answers are muddled English.
"The better English is, the worst is Mathematical meaning and Educational value of such "inventions".
Precise and exact illustration.
Simply former English teacher tries to work as a mathematician. Clear as a day.
There are at least three big English errors in those four sentences!
1) Using superlative when comparative adjective is needed
2) Using an adverb when an adjective is called for.
3) Misquoting an English idiom.
I won't mention the incomplete sentence which may have been complete in the original context.

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