Mathematics: Across country runner covers 2.5 miles in 12.5 minutes what is the runners average speed in miles per hour

Across country runner covers 2.5 miles in 12.5 minutes

Ответ:

chasen11

06.01.2022

Mathematics

Answer:

The average speed of the runner is 12 miles per hour.

Step-by-step explanation:

Given:

A cross country runner Covers =2.5 miles

Time Taken = 12.5 minutes

To Find:

The runners average speed in miles per hour=?

Solution:

Now, we know that,

Distance = speed x time

Then, 2.5 miles = average speed x 12.5 minutes

=> $\frac{5}{2} miles = \text{{average speed}} \times \frac{25}{2} minutes$

=> $\frac{5}{2} miles = \text{{average speed}}\times\frac{25}{2} \times \frac{1}{60} hours$

=> $\frac{5}{2} = \text{{average speed}}\times \frac{ 5}{2} }\times \frac{1}{12} hours$

=> $1 = \text{{average speed}} \times\frac{1}{12}$

=>average speed = 12

Hence, the average speed of the runner is 12 miles per hour.

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Ответ:

gachaperson123

04.06.2021

Mathematics

Step-by-step explanation:

At the time t = 0, population of the town = 5000

Rate of population increase = 500 per year

Therefore, the equation that will represent the population will be

$P_{t}=P_{0}+500t$

Where $P_{t}$ = Population after t years

$P_{0}$ = Initial population

t = Time in years

a). For double once the population will be 500×2 = 10000

By plugging in the values in the equation,

10000 = 5000 + 500t

500t = 10000 - 5000

500t = 5000

t = $\frac{5000}{500}$

t = 10 years

For Double twice,

Population will be = 10000×2 = 20000

Now we plug in the values in the equation again

20000 = 5000 + 500t

500t = 20000 - 5000

500t = 15000

t = $\frac{15000}{500}$

t = 30 years

For double thrice,

Population of the town = 20000×2 = 40000

Now we plug in the values in the equation,

40000 = 5000 + 500t

500t = 40000 - 5000

500t = 35000

t = $\frac{35000}{500}$

t = 70 years

b). If the population growth is 5%.

Then the growth will be exponential represented by

$T_{n}=T_{0}(1+\frac{r}{100})^{t}$

$T_{n}$ = Population after t years

$T_{0}$ = Initial population

t = time in years

For double once,

Population after t years = 10000

$10000=5000(1+\frac{5}{100})^{t}$

$(1.05)^{t}=\frac{10000}{5000}$

$(1.05)^{t}=2$

Take log on both the sides

$log(1.05)^{t}=log2$

tlog(1.05) = log2

t = $\frac{log2}{log1.05}$

t = 14.20 years

For double twice,

Population after t years = 20000

$20000=5000(1+\frac{5}{100})^{t}$

$(1.05)^{t}=\frac{20000}{5000}$

$(1.05)^{t}=4$

Take log on both the sides

$log(1.05)^{t}=log4$

tlog(1.05) = log4

t = $\frac{log4}{log1.05}$

t = 28.413 years

For double thrice

Population after t years = 40000

$40000=5000(1+\frac{5}{100})^{t}$

$(1.05)^{t}=\frac{40000}{5000}$

$(1.05)^{t}=8$

Take log on both the sides

$log(1.05)^{t}=log8$

tlog(1.05) = log8

t = $\frac{log8}{log1.05}$

t = 42.620 years

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Across country runner covers 2.5 miles in 12.5 minutes what is the runners average speed in miles per hour

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