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garri49 [273]
2 years ago
11

Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reac

h their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
Mathematics
1 answer:
dsp732 years ago
3 0

Answer:

3:2

Explanation:

Let's call the trains A and B

Train A moves from Howrah to Patna in 9 hours

Train B moves from Patna to Howrah in 16 hours

Assuming it takes 30 miles to OR from each destination,

Then train A travels 30 miles in 9 hours

Train B travels 30 miles in 16 hours

Train A's speed is 30/9= 3.33 miles per hour

Train B's speed is 30/16= 1.88 miles per hour

Ratio of their speeds(approximately,train A to train B)= 3:2

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Part 1: The equation of the line is y=2x+1

Part 2: The equation of the line in slope intercept form is y=-3x-1

Explanation:

Part 1: It is given that the point A is (1,3) and the line B is y=2 x-2

To determine the line passing through the point A and parallel to line B, let us first determine the slope and y-intercept.

From the equation of line B, the slope is m=2

Substituting the point (1,3) and m=2 in slope intercept form y=mx+b, we have,

3=2(1)+b

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1=b

Thus, the y-intercept is b=1

Let us substitute the values m=2 and b=1 in the slope intercept form y=mx+b, we get,

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Thus, the equation of the line passing though point A and parallel to line B is y=2x+1

Part 2: The given two coordinates are (-1,2) and (1,-4)

To determine the equation of line in slope intercept form, first we shall find the slope and y-intercept.

From the graph, we can see that the line touches the y-axis at -1.

Hence, the y-intercept is b=-1

The formula for slope is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

Substituting the coordinates (-1,2) and (1,-4), we have,

m=\frac{-4-2}{1+1} =\frac{-6}{2} =-3

Thus, the slope is m=-3

Substituting the values b=-1 and m=-3 in the slope intercept formula y=mx+b, we get,

y=-3x-1

Thus, the equation of the line in slope intercept form is y=-3x-1

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Step-by-step explanation:

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