Time,Speed,distance
- Thread starter dwars
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- Apr 12, 2005
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30 m / 36 mph = 0.83333 hrs = 50 minutes
30 m / 45 mph = 0.66667 hrs = 40 minutes
Yup. That's 10 minutes.
30 m / 24 mph = 1.25 hrs
30 m / 30 mph = 1.00 hrs
Nope. That's 15 minutes.
What is intended by [math]\dfrac{5\cdot 10}{4\cdot 40} = \dfrac{50}{40}[/math]. That could make more sense.
30 m / 45 mph = 0.66667 hrs = 40 minutes
Yup. That's 10 minutes.
30 m / 24 mph = 1.25 hrs
30 m / 30 mph = 1.00 hrs
Nope. That's 15 minutes.
What is intended by [math]\dfrac{5\cdot 10}{4\cdot 40} = \dfrac{50}{40}[/math]. That could make more sense.
This belongs in the "beginning algebra" forum rather than the "probability and statistics" forum.
Thank you very much for submitting your work.
Let a = anna's speed miles per minute and
j = jack's speed in miles per minute.
Why did I use miles per minute?
But it is given that [MATH]j = a + a * \dfrac{1}{4} = \dfrac{5a}{4}.[/MATH]
Follow that?
Let t = jack's time in minutes. Thus anna's time in minutes = t + 10
Speed times time equals distance. With respect to jack:
[MATH]j * t = 30 \implies t = 30 \div j =\\ 30 \div \dfrac{5a}{4} = \dfrac{30}{1} * \dfrac{4}{5a} = \dfrac{24}{a}.[/MATH]Follow that?
With respect to anna:
[MATH]a * (t + 10) = 30 \implies a * \dfrac{24}{a} + 10a = 30 \implies \\ 24 + 10a = 30 \implies 10a = 30 - 24 = 6 \implies a = \dfrac{6}{10} = \dfrac{3}{5}.[/MATH]So 3/5 of a mile per minute equates to what in miles per hour? Obviously
[MATH]\dfrac{3}{5} * 60 = 36[/MATH] miles per hour.
So the answer is 36 miles per hour.
Let's check. So jack's speed in miles per minute is
[MATH]j = \dfrac{5}{4} * \dfrac{3}{5} = \dfrac{3}{4}[/MATH] miles per minute.
So 3/5 of a mile per minute equates to what in miles per hour? Obviously
Obviously
[MATH]\dfrac{3}{4} * 60 = 45[/MATH] miles per hour.
Going at 3/4 of a mile per minute, how long in minutes does it take jack to go 30 miles?
[MATH]30 \div \dfrac{3}{4} = \dfrac{30}{1} * \dfrac{4}{3} = 40 \text { minutes.}[/MATH]
But anna's speed is 3/5 of a mile per minute. Going at 3/ of a mile per minute, how long in minutes does it take anna to go 30 miles?
[MATH]30 \div \dfrac{3}{5} = \dfrac{30}{1} * \dfrac{5}{3} = 50 \text { minutes.}[/MATH]
[MATH]50 - 40 = 10 \ \checkmark[/MATH]
It checks.
Thank you very much for submitting your work.
Let a = anna's speed miles per minute and
j = jack's speed in miles per minute.
Why did I use miles per minute?
But it is given that [MATH]j = a + a * \dfrac{1}{4} = \dfrac{5a}{4}.[/MATH]
Follow that?
Let t = jack's time in minutes. Thus anna's time in minutes = t + 10
Speed times time equals distance. With respect to jack:
[MATH]j * t = 30 \implies t = 30 \div j =\\ 30 \div \dfrac{5a}{4} = \dfrac{30}{1} * \dfrac{4}{5a} = \dfrac{24}{a}.[/MATH]Follow that?
With respect to anna:
[MATH]a * (t + 10) = 30 \implies a * \dfrac{24}{a} + 10a = 30 \implies \\ 24 + 10a = 30 \implies 10a = 30 - 24 = 6 \implies a = \dfrac{6}{10} = \dfrac{3}{5}.[/MATH]So 3/5 of a mile per minute equates to what in miles per hour? Obviously
[MATH]\dfrac{3}{5} * 60 = 36[/MATH] miles per hour.
So the answer is 36 miles per hour.
Let's check. So jack's speed in miles per minute is
[MATH]j = \dfrac{5}{4} * \dfrac{3}{5} = \dfrac{3}{4}[/MATH] miles per minute.
So 3/5 of a mile per minute equates to what in miles per hour? Obviously
Obviously
[MATH]\dfrac{3}{4} * 60 = 45[/MATH] miles per hour.
Going at 3/4 of a mile per minute, how long in minutes does it take jack to go 30 miles?
[MATH]30 \div \dfrac{3}{4} = \dfrac{30}{1} * \dfrac{4}{3} = 40 \text { minutes.}[/MATH]
But anna's speed is 3/5 of a mile per minute. Going at 3/ of a mile per minute, how long in minutes does it take anna to go 30 miles?
[MATH]30 \div \dfrac{3}{5} = \dfrac{30}{1} * \dfrac{5}{3} = 50 \text { minutes.}[/MATH]
[MATH]50 - 40 = 10 \ \checkmark[/MATH]
It checks.