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3 years ago

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Henry and Gavin are marking exam papers. Each set takes Henry 36 minutes and Gavin 1 hour. Express the times Henry and Gavin tak

e as a ratio.
Give your answer in its simplest form.

1 answer:

RUDIKE [14]3 years ago

6 0

The ratio of time taken by Henry to time taken by Gavin is 3:5

Step-by-step explanation:

Time taken by Henry for each set = 36 minutes

Time taken by Gavin for each set = 1 hour

We will convert Gavin's time into minutes.

Time taken by Gavin for each set = 60 minutes

Ratio;

Time taken by Henry : Time taken by Gavin

$36:60$

Dividing by 6

$\frac{36}{6}:\frac{60}{6}\\6:10$

Dividing by 2

$\frac{6}{2}:\frac{10}{2}\\3:5$

The ratio of time taken by Henry to time taken by Gavin is 3:5

Keywords: ratio, division

Learn more about ratios at:

#LearnwithBrainly

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Answer:

It takes 1 week for the ant population to double

It takes 1.58 weeks for the ant population to triple

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Step-by-step explanation:

It takes only 1 week for the population to double from 300 to 600

We can model the population of ant (or anteater) as the following:

$p = ae^{kt}$

Where a = 300 is the initial population at t = 0

When t = 1, P = 600

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$e^k = 2$

k = ln2 = 0.693

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t = 1.1/k = 1.1/0.693 = 1.58 weeks.

When there are 10000 ants on board, p = 10000:

$300e^{kt} = 10000$

$e^{kt} = 10000/300 = 33.33$

$kt = ln33.33 = 3.51$

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Similarly for anteater, at t = 0 there are 17 of them so A = 17. We can solve for their K parameter if the population doubled after 3.2 weeks

$e^{3.2K} = P/A = 2$

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At the time there are 200 ants per anteater

$p = 200P$

$300e^{kt} = 200*17e^{Kt}$

$e^{kt - Kt} = 200*17/300$

$e^{0.693t - 0.2166t} = 11.33$

$e^{0.4765t} = 11.33$

$0.4765t = ln11.33$

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Case (q=0,d=1) → n = 0 through 14 [15 possibilities]
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Case (q=0,d=7) → n = 0 through 2 [3 possibilities]
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Total from q=0 case: 1 + 3 + ... + 15 + 17 = 81

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Total from q=1 case: 2 + 4 + ... + 10 + 12 = 42

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Total from case q=2: 1 + 3 + 5 + 7 = 16

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