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3 years ago

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At 1:30 p.m., Tom leaves in his boat from a dock and heads south. He travels at a rate of 25 miles per hour. Ten minutes later,

Mary leaves the same dock in her speedboat and heads after Tom. If she travels at a rate of 30 miles per hour, when will she catch up with Tom

1 answer:

Nadya [2.5K]3 years ago

7 0

Answer: she would catch up with Tom in 1 hour.

Step-by-step explanation:

Let t represent the time it will take for Mary to catch up with Tom.

Tom leaves his boat from a dock and travels at a rate of 25 miles per hour.

Distance = speed × time

Distance travelled by Tom in t hours is

25 × t = 25t

Ten minutes later, Mary leaves the same dock in her speedboat and heads after Tom. Converting 10 minutes to hours, it becomes 10/60 hour

Time spent by Mary is (t - 10/60) hours. If she travels at a rate of 30 miles per hour, it means that the distance that she would travel in

(t - 10/60) hours is

30(t - 10/60)

= 30t - 5

By the time she catches up with Tom, they would have covered the same distance. It means that

25t = 30t - 5

30t - 25t = 5

5t = 5

t = 5/5 = 1 hour

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Answer:

$y=3.529 x +37.91$

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

$y(8) = 3.529*8 + 37.91= 66.142$

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

$y(11) = 3.529*11 + 37.91= 76.729$

Step-by-step explanation:

For this case we have the following data:

Miles Traveled x: 2,3,10,7,8,15,3,1,11

Sales y :31,33,78,62,65,61,48,55,120

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

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So we can find the sums like this:

$\sum_{i=1}^n x_i =60$

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With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=582-\frac{60^2}{9}=182$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=4329-\frac{60*553}{9}=642.33$

And the slope would be:

$m=\frac{642.33}{182}=3.529$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{60}{9}=6.67$

$\bar y= \frac{\sum y_i}{n}=\frac{553}{9}=61.44$

And we can find the intercept using this:

$b=\bar y -m \bar x=61.44-(3.529*6.67)=37.91$

So the line would be given by:

$y=3.529 x +37.91$

We can predict the sales representative travelled 8 miles replacing x =8 and we got:

$y(8) = 3.529*8 + 37.91= 66.142$

And we can predict the sales representative travelled 11 miles replacing x =11 and we got:

$y(11) = 3.529*11 + 37.91= 76.729$

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