word problems and inequalities

[jonesbetty]

please help
The formula R= -0.075+3.85 can be used to predict the world record in the 1500 meter run, t years after 1930. Determine an inequality that identifies the years the world record will be less than 3.1 minutes.

 

[soroban]

Hello, jonesbetty!

You left out the \(\displaystyle t\) . . .

\(\displaystyle \text{The formula }\,R \:=\:-0.075t + 3.85\,\text{ can be used to predict}\)
\(\displaystyle \text{the world record in the 1500-meter run, }t\text{ years after 1930.}\)

\(\displaystyle \text{Determine an inequality that identifies the }year\)
\(\displaystyle \text{the world record will be less than 3.1 minutes.}\)

Note that the year is: .\(\displaystyle y \:=\:t + 1930 \quad\Rightarrow\quad t \:=\:y - 1930\)

Substitute: .\(\displaystyle R \:=\:-0.075(y-1930) + 3.85 \quad\Rightarrow\quad R\:=\:-0.075y + 148.6\)


We want \(\displaystyle R\,<\,3.1\)

. . Therefore: .\(\displaystyle -0.075y + 148.6 \:<\:3.1\)

 

[jonesbetty]

thank you for your help

thanks so much