SOLUTION: On a particular day, the wind added 3 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 3 miles per hour from his rate on his return trip. Alfonso f
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-> SOLUTION: On a particular day, the wind added 3 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 3 miles per hour from his rate on his return trip. Alfonso f
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Question 982020: On a particular day, the wind added 3 miles per hour to Alfonso's rate when he was cycling with the wind and subtracted 3 miles per hour from his rate on his return trip. Alfonso found that in the same amount of time he could cycle 48 miles with the wind, he could go only 30 miles against the wind.What is his normal bicycling speed with no wind?
someone told me to solvie it like this
Wind speed is 3 mph.
r, Alfonso's rate when no wind.
t, time for specific what he "found".
______________________speed__________ti...
withWind______________r+3_____________t...
againstWnd____________r-3_____________t...
Uniform Travel Rates Rule: RT=D,
T=D/R
The times for with and against wind are the same t.
48 over r+3= 30 over r-3
Solve for R
But i have not idea how to solve for R. i know this probably seems easy but ive never really been good at math
You can put this solution on YOUR website! Variables:
r = rate with no wind
t = time it takes to cycle 48 miles with the wind, or 30 miles against the wind.
Table:
With Wind
Against Wind
Speed
r+3
r-3
Distance
48
30
Time
t
t
The table isn't mandatory, but it helps sort out all the data (known or unknown).
Focus on the "With Wind" column. This is where the wind helps and pushes him faster. His speed increases from r to r+3. He can go d = 48 miles. The time taken is t.
Use and the info above and solve for t
The time expression to go 48 mi with the wind is hours.
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Now move to the next column "against wind"
The wind is now slowing him down. His speed decreases from r to r-3. He can go d = 30 miles against the wind. The time taken is t because it takes the same amount of time to go 48 mi with the wind and 30 mi against the wind.
Use and the info above and solve for t
The time expression to go 30 mi against the wind is hours.
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From the two sub-parts above, we found these two equations and
Because the t values are the same, we can equate the two right hand sides to get . It doesn't matter which side what expression is on.
Now we solve for r. There are a few ways to do this. One way is to cross multiply.
Cross multiplication happens here
Question: What is his normal bicycling speed with no wind?
Answer: 13 mph
If you wanted to find the time (t), you would pick on any equation that has r and t in it. Plug in r = 13 and evaluate.
It takes him 4 hours to either go 48 mi with the wind and 30 mi against the wind. The choice of equation doesn't matter because this (r,t) pair makes both equations true at the same time. They both have the same r and t values.
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