Mathematics, 24.08.2019 00:30 sadewright21404

Two trains are 348 miles apart, and their speeds differ by 22 mph. find the speed of each train if they are traveling toward each other and will meet in 3 hours

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Answer from: ShundaBaker

Total distance between the trains = 348 miles

Total time to cross that distance by trains = 3 h.

So, sum of their speed would be: 348/3 = 116

A.T.Q,

Speed of train 1 - speed of train 2 = 22

so, two equation that has formed are:

a+b=116

a-b=22, a=b+22

Substitute that in above equation; b+22+b=116

2b= 94, b=47 & a=116-47 =69

Speed of the TRAIN IS 47 & 69 miles per hour.

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Answer from: kaliahgrey

The two trains are 348 miles apart:

Since the speed of both trains differ by 22 mph

Let the speeds be x and x + 22

Distance = Speed * time

In 3 hours the train traveling x mph would have traveled = 3*x = 3x miles.

In 3 hours the train traveling (x+22) mph would have traveled = 3*(x+22)

= 3*x + 3*22 = 3x + 66 miles.

Total = 3x + 3x + 66 = 348

3x + 3x + 66 = 348

6x + 66 = 348

6x = 348 - 66

6x = 282

x = 282/6

x = 47

Recall the speeds of each train were x, and (x + 22) mph

x = 47, x + 22 = 47 + 22 = 69

So speed of each train is 47 mph and 69 mph

I hope this helped.

Answer from: Quest

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

Answer from: Quest

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,

b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,

and solve for the variable

* lets solve the problem

∵ $7^{x}=77$

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴ $ln(7^{x})=ln(77)$

- use the rule $ln(a^{n})= nln(a)$

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴ $x=\frac{ln(77)}{ln(7)}=2.23$

* the solution of the equation is 2.23 to the nearest 2 decimal places

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Two trains are 348 miles apart, and their speeds differ by 22 mph. find the speed of each train if t...