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Svetlanka [38]
3 years ago
6

Two trains A and B are 240 miles apart. Both start at the same time and travel toward each other. They meet 3 hours later. The s

peed of train A is 20 miles faster than train B. Find the speed of each train. (SHOW WORK)
Mathematics
1 answer:
otez555 [7]3 years ago
8 0

Answer: Train A = 50 mph; Train B = 30 mph

Step-by-step explanation:

In this case, let's call the speed of both trains as:

Va: speed of train A

Vb: speed of train B

As train A is faster than train B, let's call speed of train B as X; So if Vb is X, then Va would be:

Vb = X

Va = X + 20

If we combine both Speed, we have:

V = Va + Vb = X + X + 20 = 2X + 20

Now that we have an expression for the combined speed, let's recall the formula for speed in general:

V = d/t

Where:

d: distance = 240 miles

t: time = 3 hours

Combining all the data we have:

V = 240/3

but V is 2X + 20 so:

2X + 20 = 240/3

Solving for X:

2X + 20 = 80

2X = 80 - 20

2X = 60

X = 60/2

X = Vb = 30 mph

Now that we know speed of one train, we can know the speed of the other train:

Va = 30 + 20 = 50 mph

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5 0
2 years ago
Given: cos α = 4/5, sin β= 4/5, and α and β are both in quadrant 1. find sin (α+β)
mezya [45]
We have the formula (sin x)^2 + (cos x)^2 = 1;
Then, sin α = \sqrt{1-  ( \frac{4}{5}) ^{2} } =  \frac{3}{5} ;
cos β = \sqrt{1- ( \frac{4}{5}) ^{2} } = \frac{3}{5} ;
We apply the formula sin ( α + β ) = sin α x cos β + sin β x cos α = (3/5)x(4/5) + (4/5)x(3/5) = 12/25 + 12/25 = 24/25;
8 0
3 years ago
A recipe for 8 servinfs of pudding clls for 2 cups of milk.How many gallons of milk are needed to make enough pudding for 64 ser
I am Lyosha [343]
In order to solve this, we first need to know what the ratio of servings of pudding to cups of milk is. We can see that 8 servings of pudding requires 2 cups of milk, so the ratio is 8/2, which can be reduced to 4/1. This means that for every 4 servings of pudding, we will be adding 1 cup of milk. So all we need to do to find out how many cups would be needed for 64 servings of pudding, we simply need to divide by 4.

64 / 4 = 16

So for 64 servings of pudding, we will need 16 cups of milk. But that's not what the question wants to know, it wants to know how many gallons of milk it would need. 

In order to find that out, we have to know how many cups there are in one gallon. There are 2 cups in one pint, there are 2 pints in a quart, and there are 4 quarts in a gallon, so we just have to multiply those numbers, and we get 4 * 2 * 2 = 8 * 2 = 16

There are 16 cups in one gallon, therefore, 64 servings of pudding will require 1 gallon of milk.
Hope that helped! =)
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3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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