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Leni [432]
3 years ago
8

The average speed of an express train is 15 mi/h faster than the average speed of a local train 2 hours longer than the express

train to cover 360 miles. what is the average speed of the express train?
PLEASE HELP!!!!
Mathematics
1 answer:
natta225 [31]3 years ago
5 0
360÷15×2=48hrs of the express train.
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A boat on a river travels downstream between two points, 90 mi apart, in 1 h. The return trip against the current takes 2 1 2 h.
docker41 [41]

Answer:

A)63miles per hour.

B)27 miles per hour

Step-by-step explanation:

HERE IS THE COMPLETE QUESTION

boat on a river travels downstream between two points, 90 mi apart, in 1 h. The return trip against the current takes 2 1 2 h. What is the boat's speed (in still water)??b) How fast does the current in the river flow?

Let the speed of boat in still water = V(boat)

speed of current=V(current)

To calculate speed of boat downstream, we add speed of boat in still water and speed of current. This can be expressed as

[V(boat) +V(current)]

It was stated that it takes 1hour for the

boat to travels between two points of 90 mi apart downstream.

To calculate speed of boat against current, we will substact speed of current from speed of boat in still water. This can be expressed as

[V(boat) - V(current)]

and it was stated that it takes 2 1/2 for return trip against the Current

But we know but Speed= distance/time

Then if we input the stated values we have

V(boat) + V(current)]= 90/1 ---------eqn(1)

V(boat) - V(current) = 90/2.5----------eqn(2)

Adding the equations we have

V(boat) + V(current) + [V(boat) - V(current)]= 90/2.5 + 90/1

V(boat) + V(current) + V(boat) - V(current)]=90+36

2V(boat)= 126

V(boat)=63miles per hour.

Hence, Therefore, the speed of boat in still water is 63 miles per hour.

?b) How fast does the current in the river flow?

the speed of the current in the river, we can be calculated if we input V(boat)=63miles per hour. Into eqn(1)

V(boat) + V(current)]= 90/1

63+V(current)=90

V(current)= 27 miles per hour

Hence,Therefore, the speed of current is 27 miles per hour.

7 0
3 years ago
Find the sum of the first one hundred positive integers. see fig 6.26
nignag [31]
Here's a pattern to consider:
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.

Quick note
We can use a formula to find out the sum of an arithmetic series:
s =  \frac{n(n + 1)}{2}
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.
8 0
3 years ago
Simplify the product using the distributive property. (-4h +2)(3h +7)
Alekssandra [29.7K]

Answer:

  A.  -12h² - 22h + 14

Step-by-step explanation:

(-4h +2)(3h +7) = -4h(3h +7) +2(3h +7) . . . . . . . (a +b)c = ac +bc

  = (-4h)(3h) + (-4h)(7) + (2)(3h) + (2)(7) . . . . . . . a(b +c) = ab +ac . . . (twice)

  = -12h² -28h +6h +14

  = -12h² -22h +14 . . . . . . . . collect terms

3 0
3 years ago
What is the length of segment A’B with the scale factor of 2
Nata [24]
260 units are the answer
7 0
3 years ago
Find the sum of three consecutive odd integers where x is the greatest integer
myrzilka [38]
X + (x − 2) + (x − 4) = ? ;  In which
<span>
x + x </span>− 2 + x − 4 ; 

Combine the "like terms" ; 

  x + x + x = 3x ; 

  − 2 − 4  =  −6 ; 

So we have:  "3x  − 6" as the sum. ;
___________________________
The sum of three consecutive odd integers, in which "x" is the greatest integer;  is:  "3x − 6" .
_____________________________________________
Note:  The three consecutive odd integers, from least to greatest, are:

"(x − 4)" , "(x − 2)" , and "x" .

The sum is:  "(3x  − 6)<span>" .
</span>_____________________________________________
Note:  "(3x  − 6)" factors into:  " 3(x −2)" .

Note that:  " (x − 2) " is the second integer.
______________________________________________
So the sum total, which is:  "(3x  −  6)" ;  is 3 (three) times the value of the second integer; that is, "3 (x − 2)" .
______________________________________________
5 0
2 years ago
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