If an average-sized man with a parachute jumps from an airplane, he will fall 
F(t)=12.5(0.2t−1)+20t
 feet in t seconds. How long will it take him to fall 150 feet?

We are given the function for the distance fallen by a man with a parachute as:

\[
F(t) = 12.5(0.2t - 1) + 20t
\]

We are tasked with finding the time \( t \) when the man has fallen 150 feet, so we set \( F(t) = 150 \) and solve for \( t \):

\[
150 = 12.5(0.2t - 1) + 20t
\]

### Step 1: Expand the expression
First, distribute the 12.5:

\[
150 = 12.5(0.2t) - 12.5 + 20t
\]
\[
150 = 2.5t - 12.5 + 20t
\]

### Step 2: Combine like terms
Combine the \( t \)-terms:

\[
150 = (2.5t + 20t) - 12.5
\]
\[
150 = 22.5t - 12.5
\]

### Step 3: Solve for \( t \)
Add 12.5 to both sides:

\[
150 + 12.5 = 22.5t
\]
\[
162.5 = 22.5t
\]

Now, divide by 22.5:

\[
t = \frac{162.5}{22.5} \approx 7.22 \text{ seconds}
\]

So, it will take approximately **7.22 seconds** for the man to fall 150 feet.

---

Would you like more details on any step or have any other questions? Here are some related questions to explore:

1. How would the equation change if the man falls 200 feet?
2. What happens to the fall if the parachute opens and reduces the speed?
3. What is the instantaneous velocity at any time \( t \)?
4. How would this change if the fall happened on another planet with different gravity?
5. How long would it take to fall 300 feet?

**Tip**: Always check units in word problems to ensure you interpret them correctly (feet, seconds, meters, etc.).

If an average-sized man with a parachute jumps from an airplane, he will fall F(t)=12.5(0.2t−1)+20t feet in t seconds. How long will it take him to fall 150 feet?

Find out how to calculate the time it takes for a man with a parachute to fall 150 feet using the equation F(t) = 12.5(0.2t−1)+20t. This step-by-step solution covers algebraic concepts and solving linear equations, ideal for students in Grades 9-12.

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