distance formula

[popeyesmom]

I am having problems completing this math problem. Would you please explain in step by step instructions. Thank you.
Nolan Ryan was famous for pitching a baseball at speeds that exceeded 100 miles per hour. How long would a baseball take to travel 60 feet 6 inches--the distance from the pitcher's rubber to home plate--at a a speed of 100 miles per hour?

 

[soroban]

Hello, popeyesmom!

We need a procedure for converting units of measure.

Nolan Ryan was famous for pitching a baseball at speeds that exceeded 100 miles per hour.
How long would a baseball take to travel 60 feet 6 inches, the distance from the pitcher's rubber
to home plate, at a a speed of 100 miles per hour?

First, convert miles-per-hour to feet-per-second.

"100 miles per hour" means: .\(\displaystyle \dfrac{\text{100 miles}}{\text{1 hour}}\)

Since \(\displaystyle \text{1 mile} = \text{5280 feet}\), we can multiply by \(\displaystyle \dfrac{\text{5280 feet}}{\text{1 mile}}\;\) which equals 1.

Since \(\displaystyle \text{1 hour} = \text{3600 seconds}\), we can multiply by \(\displaystyle \dfrac{\text{1 hour}}{\text{3600 sec}}\;\) which equals 1.


We have: .\(\displaystyle \dfrac{100\;\text{miles}}{1\;\text{hour}} \times \dfrac{5280\text{ ft}}{1\;\text{mile}} \times \dfrac{1\;\text{hour}}{3600\;\text{sec}}\)


Note how the units cancel:

. . \(\displaystyle \dfrac{100\;\rlap{/////}{\text{miles}}}{1\;\rlap{////}\text{hour}} \times \dfrac{5280\text{ ft}}{1\;\rlap{////}\text{mile}} \times \dfrac{1\;\rlap{////}\text{hour}}{3600\;\text{sec}} \;=\;\dfrac{100\cdot5280\text{ ft}}{3600\text{ sec}}\)

Reduce the fraction: .\(\displaystyle \dfrac{44\text{ ft}}{3\text{ sec}} \:=\:\dfrac{44}{3}\text{ ft/sec}\)


Formula: .\(\displaystyle \text{(Distance)} \:=\:\text{(Speed)} \times \text{(Time)} \quad\Rightarrow\quad T \:=\:\dfrac{D}{S}\)

Therefore: .\(\displaystyle T \;=\;\dfrac{60.5\text{ ft}}{\frac{44}{3}\text{ ft/sec}} \;=\;\dfrac{33}{80} \;=\;0.4125\text{ sec} \)