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Serhud [2]
3 years ago
14

James drove 986 miles from Philadelphia to Orlando in 14.5 hours. He continued to drive at the same average speed and drove anot

her 714 miles. What is the total amount of time James spent driving from Philadelphia to New Orleans?
Mathematics
1 answer:
VMariaS [17]3 years ago
6 0

Answer:

James Spent 25 hours driving from  Philadelphia to New Orleans.

Step-by-step explanation:

Given:

Distance from Philadelphia to Orlando = 986 miles

Time required to travel Philadelphia to Orlando = 14.5 hrs

Distance from Orlando to New Orleans = 714 mile.

We need to find the total amount of time James spent driving from Philadelphia to New Orleans.

Solution:

First we will find the average speed from Philadelphia to Orlando.

We know that;

Speed is equal to distance divided by time.

framing in equation form we get;

average speed from Philadelphia to Orlando = \frac{986}{14.5}=68\ mi/hrs

Now given that he traveled with same speed from Orlando to New Orleans.

So we will find the time required from Orlando to New Orleans.

We know that;

Time is equal to Distance divided by speed.

framing in equation form we get;

time required from Orlando to New Orleans = \frac{714}{68}= 10.5 \ hrs

Now we will find the total time James spent on driving from Philadelphia to New Orleans.

the total time James spent on driving from Philadelphia to New Orleans is equal to sum of Time required to travel Philadelphia to Orlando and time required from Orlando to New Orleans.

framing in equation form we get;

the total time James spent on driving from Philadelphia to New Orleans = 14.5 + 10.5 = 25 hours.

Hence James Spent 25 hours driving from  Philadelphia to New Orleans.

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<h2>Answer:</h2>

ABCD is a trapezoid

<h2>Step-by-step explanation:</h2>

<em>Given points of the quadrilateral:</em>

A(8,21),B(10,27),C(26,26) and D(18,2)

To show whether ABCD is a trapezoid, we find a pair of parallel sides in ABCD. If two of its sides are parallel to each other then ABCD is a trapezoid.

<em>Step 1:</em> With the given points, sketch a graph. The diagram is attached to this response.

<em>Step 2:</em> As shown in the diagram, the two sides that are likely to be parallel are AB and CD

If these two sides have same gradient/slope, then the quadrilateral is a trapezoid.

Now calculate the slopes of those sides using the slope formula;

m = \frac{y_2 - y_1}{x_2 - x_1}

<em>Calculate the slope of AB </em>(where x₁ = 8, y₁ = 21, x₂ = 10, y₂ = 27)

m(AB) = \frac{27-21}{10-8}

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<em>Calculate the slope of CD </em>(where x₁ = 26, y₁ = 26, x₂ = 18, y₂ = 2)

m(CD) = \frac{2-26}{18-26}

m(CD) = \frac{-24}{-8}

m(CD) = 3

Since the two slopes - m(AB) and m(CD) slopes are equal to 3, the quadrilateral ABCD is a trapezoid.

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