While scuba diving Quentin descended 2 1/3 feet each second for 30 seconds. If Quentin ended up at a depth of -234 feet before he began his descent, what was his original depth?
Do I multiply 2 1/3ft by 30 seconds?
Yes. That's the first step.
Then do I add that 70 to -243
Right.
To find Quentin's original depth, you need to calculate his total descent during the 30 seconds.
First, convert the mixed number 2 1/3 to an improper fraction. This can be done by multiplying the whole number (2) by the denominator (3) and adding the numerator (1), then placing the sum over the denominator:
2 * 3 + 1 = 6 + 1 = 7
7/3
Now, multiply the descent rate per second (7/3 ft) by the duration of the descent (30 seconds):
7/3 ft * 30 = 210/3 ft
Next, subtract the total descent (210/3 ft) from the final depth (-234 ft) to find the original depth:
Original depth = -234 ft - (210/3 ft)
To subtract mixed numbers, it helps to convert them to improper fractions.
-234 ft = -234/1 ft
To perform the subtraction, make the denominators the same (3):
-234/1 ft - (210/3 ft) = -234/1 ft - (210/3 * 1/1 ft) = -234/1 ft - 630/3 ft
Now that the denominators are the same, combine the numerators:
-234/1 ft - 630/3 ft = (-234 - 630)/1 ft
Subtract the numerators:
-234 - 630 = -864
The final result is -864/1 ft, which means Quentin's original depth was -864 feet.