A flea 1/16 of an inch tall can jump 9 3/8 inches high. If a person five feet tall could jump like a flea, how high could she jump? Careful: Feet are not inches.
The solution I posted earlier gives you the answer in feet.
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A flea is only about 1/16 of an inch tall but can jump 8 inches high if a human could jump as high in proportion to its height as a flea can, how high could a 5-foot-tall human jump
To find out how high a person five feet tall could jump if they could jump like a flea, we can convert the height of the flea's jump into a common unit, such as inches.
Since the flea's height is given as 1/16 of an inch and its jump height is 9 3/8 inches, we need to add these two values.
1/16 + 9 3/8
First, let's convert the mixed number 9 3/8 to an improper fraction.
9 3/8 = (8 * 9 + 3) / 8 = 75/8
Now we can add the two fractions:
1/16 + 75/8
To add these fractions, we need a common denominator, which is 16 * 8 = 128.
(1/16 * 8/8) + 75/8 = 8/128 + 75/8
Now add the fractions:
8/128 + 75/8 = (8 + 1200) / 128 = 1208/128
Simplifying the fraction:
1208/128 = 9 104/128
Now we have the height of the flea's jump as 9 104/128 inches.
Since there are 12 inches in a foot, we can divide the flea's jump height by 12 to convert it to feet:
(9 104/128) / 12 = (1168 + 104/128) / 12 = 1272/128 / 12
Simplifying further:
1272/128 = 9 96/128
So, when a person who is five feet tall could jump like a flea, they would be able to jump approximately 9 feet and 96/128 feet high.
Simplifying the mixed number:
9 96/128 = 9 3/4 feet
Therefore, a person who is five feet tall and could jump like a flea would be able to jump approximately 9 and 3/4 feet high.
To solve this problem, we need to convert the person's height from feet to inches. 1 foot is equal to 12 inches, so a person who is 5 feet tall would be 5 x 12 = 60 inches tall.
Now, we can set up a proportion to find out how high the person could jump if they could jump like a flea. The proportion can be set up as:
(Height of flea) / (Height of person) = (Jumping ability of flea) / (Jumping ability of person)
Let's fill in the values given in the question:
(1/16 inch) / (60 inches) = (9 3/8 inches) / (x inches)
To solve for x, we can cross multiply:
1/16 * x = 60 * (9 3/8)
To multiply 60 by 9 3/8, we need to convert the mixed number (9 3/8) to an improper fraction. This can be done by multiplying the whole number (9) by the denominator (8) and adding the numerator (3) to get the new numerator (75). So, 9 3/8 can be converted to 9 3/8 = 9 + 3/8 = 75/8.
Now, the equation becomes:
1/16 * x = 60 * (75/8)
To simplify the right side, we multiply 60 by 75 and divide the result by 8:
1/16 * x = (60 * 75) / 8
Multiply 60 by 75:
1/16 * x = 4500 / 8
Divide 4500 by 8:
1/16 * x = 562.5
To isolate x, the variable representing the height the person could jump, we multiply both sides by 16 (the reciprocal of 1/16):
x = 562.5 * 16
x = 9000
Therefore, if a person who is 5 feet tall could jump like a flea, they would be able to jump approximately 9000 inches high.