<span>A freight train completes its journey of 150 miles 1 hour earlier if its original speed is increased by 5 miles/hour. What is the train’s original speed?
***
let x=original speed
x+5=increased speed
travel time=distance/speed
..
lcd:x(x+5)
150(x+5)-150x=x(x+5)
150x+750-150x=x^2+5x
x^2+5x-750=0
(x-25)(x+30)=0
x=25
What is the train’s original speed? 25 mph</span>
Answer:
10 and 42
Step-by-step explanation:
The difficulty with word problems is translating them into math.
Let's do that
---------------------
The sum of a number and two times a smaller number is 62.
let's call the bigger number b, and the smaller number s
b + 2s = 62
Three times the bigger number exceeds the smaller number by 116
3b = s + 116
-----------------------
Now manipulate one of the equations to isolate the variable
3b = s + 116
Subtract 116 from both sides
3b - 116 = s
substitute for s = 3b - 116 in
b + 2s = 62
b + 2(3b - 116) = 62
Distribute
b + 6b - 232 = 62
combine like terms
7b = 294
Divide both sides by 7
b = 42
to find s plug in b = 42 into
b + 2s = 62
42 + 2s = 62
subtract 42 from both side
2s = 20
divide both sides by 2
s = 10
Answer:
c
Step-by-step explanation:
count
Which number is the under lined digit?
<h3><em>In AP form 2nd term - 1st term = 3rd term - 2nd term
</em></h3><h3><em>b²-a² = c²-b²
</em></h3><h3><em>b²+b² = c²+a²
</em></h3><h3><em>2b² = c²+a²
</em></h3><h3><em>
</em></h3><h3><em>Add 2ab+2ac+2bc on both sides
</em></h3><h3><em>
</em></h3><h3><em>2b²+2ab+2ac+2bc = a²+c²+ac+ac+bc+bc+ab+ab
</em></h3><h3><em>2b²+2ab+2ac+2bc = ac+bc+a²+ab+bc+c²+ab+ac
</em></h3><h3><em>2b²+2ab+2ca+2cb = ca+cb+a²+ab+cb+c²+ab+ac
</em></h3><h3><em>2(ba+b²+ca+cb) = (ca+cb+a²+ab) + (cb+c²+ab+ac)
</em></h3><h3><em>2((ba+b²)+(ca+cb)) = ((ca+cb)+(a²+ab)) + ((cb+c²)+(ab+ac))
</em></h3><h3><em>2(b(a+b)+c(a+b)) = (c(a+b)+a(a+b)) + (c(b+c)+a(b+c)) </em></h3><h3><em>2(b+c)(a+b) = (c+a)(a+b) + (c+a)(b+c)
</em></h3><h3><em>
</em></h3><h3><em>Divide whole by (a+b)(b+c)(c+a)</em></h3><h3><em></em></h3><h3><em>2/c+a = 1/b+c + 1/a+b</em></h3><h3><em>1/c+a + 1/c+a = 1/b+c + 1/a+b</em></h3><h3><em>1/c+a - 1/b+c = 1/a+b - 1/c+a</em></h3><h3><em></em></h3><h3><em>2nd term - 1st term = 3rd term - 2nd term
</em></h3><h3><em>Thus 1/b+c, 1/c+a, 1/a+b are in AP.</em></h3><h3><em></em></h3><h3><em>HOPE IT HELPS !!!</em></h3><h3><em>THANK YOU !!!</em></h3>
