Average MPH question.

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Giaruso

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Not sure I am on the correct forum; since, I do not know where this question fits. If my problem is solved here, will s/he who solves it please show me the arithmetical steps so I can solve other similar combinations on my own. Thanks so much.

My question:

"On a 30-mile bike ride, I averaged 14.4 mph overall, while averaging only 12.9 mph for the first 11 miles. What did I average for the remaining 19 miles to arrive the overall 14.4 mph?
 
Giaruso said:
Not sure I am on the correct forum; since, I do not know where this question fits. If my problem is solved here, will s/he who solves it please show me the arithmetical steps so I can solve other similar combinations on my own. Thanks so much.

My question:

"On a 30-mile bike ride, I averaged 14.4 mph overall, while averaging only 12.9 mph for the first 11 miles. What did I average for the remaining 19 miles to arrive the overall 14.4 mph?
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You rode 30 miles at 14.4 mph so how many hours did that take?

You rode the first 11 miles at 12.9 mph so how many hours did that take?

How many hours did it take to ride the last 19 miles? 19 miles in that many hours is what speed?
 
HallsofIvy said:
You rode 30 miles at 14.4 mph so how many hours did that take?

You rode the first 11 miles at 12.9 mph so how many hours did that take? 51 minutes

How many hours did it take to ride the last 19 miles? 74 minutes

19 miles in that many hours is what speed?
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19 miles divided by 74 minutes x 60 = 15.4 MPH (for the 19 mile section)

I believe that is correct. Thanks so much.

Denny G.
 
Denis said:
You missed my point; was hinting at a "general case" formula:

a=initial distance(11), b = remaining distance(19), c = total distance(30)
x=avg. speed for x(12.9), y = avg. speed for y(?), z = avg. speed for z(14.4)

General case formula:
ax + by = cz

With yours:
y = (cz - ax) / b

The "given" can be any one of the 6 variables; solve similarly.
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I believe I got your point this time, sorry. The "with yours" formula is exactly what I was looking for. I took one high school semester of Algebra waaaay back in the early 50s. I realize this is a rather simple problem, and I could have figured it out--eventually, but with all this fine Internet help, as yours, one gets a little lazy. Thank you very much. Oh, by the way, I lived in Streetsville, Ontario in the early 50s, but have lived in southern California since 1953. I will be paying my first visit to Quebec next year about this time via a cruise out of Boston. If I run into you, I'll buy you a drink.:p
 
Giaruso said:
Well, I'll say one thing, no one here seems to be an Alzheimer's victim, that's for sure. Great group!
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I can remember what I learned in high school- I just can't remember where I put my glasses this morning.
 
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