Answer:
5.1 mph
Step-by-step explanation:
she ran 3 2/5 miles in 2/3 hours.
that is the essential information to solve the problem. everything else is just there to give you "atmosphere" and Shao to confuse you.
the question is simply : what was her speed in mph ?
that means we need to bring the ratio of
3 2/5 miles / 2/3 hours
to 1 hour in the denominator (instead of 2/3 hours).
because we need that to express miles per (one) hour.
so, what do we need to multiply 2/3 with to get 1 (=3/3) ?
2/3 × x = 1
2x = 3
x = 3/2
so, to get 1 hour, we need to multiply the denominator by 3/2.
and to keep the original value of the ratio, we need to multiply also the numerator by the same 3/2.
speed = (3 2/5 miles × 3/2) / (2/3 hours × 3/2) =
= (17/5 miles × 3/2) / (1 hour) = 51/10 miles / 1 hour =
= 5.1 miles / 1 hour = 5.1 mph
Method 1
Applying the Pythagorean Theorem
we know that
Solve for a
therefore
<u>the answer is</u>
the length of the altitude is 
Method 2
we know that
-------> equation A
and
in this problem
--------> equation B
equate equation A and equation B
therefore
the answer is
the length of the altitude is
Since the first number is 1, it will remain 1 at the end. So we have to find the bottom number to the power of four.
This can be simplified to equal
Which equals to 16. So we know the final equation will be equal to
1/16
24 because if the sum is 72 you divide 72 by 3 and you get 24
If we consider the first half mile to be charged at $0.30 per tenth also, that half-mile costs $1.50 and the charges amount to a fixed fee of $2.00 and a variable fee of $0.30 per tenth mile.
After you subtract the $2 tip and the fixed $2 fee from the trip budget amount, you have $11.00 you can spend on mileage charges. At 0.30 per tenth mile, you can travel
... $11.00/$0.30 = 36 2/3 . . . . tenth-miles
The trip is measured in whole tenths, so you can ride ...
... 36 × 1/10 = 3.6 miles
_____
If you want to see this in the form of an equation, you can let x represent the miles you can travel. Then your budget amount gives rise to the inequality ...
... 3.50 + 0.30((x -.50)/0.10) + 2.00 ≤ 15.00
... 3.50 + 3x -1.50 +2.00 ≤15.00 . . . . . . . eliminate parentheses
... 3x ≤ 11.00 . . . . . . . . . . . . . . . . . . . . . . . . collect terms, subtract 4
... x ≤ 11/3 . . . . . . . . . . . . . . . . . . . . . . . . . . divide by 3
... x ≤ 3.6 . . . . . rounded down to the tenth
