LINEAR EQUATIONS AND INEQUALITIES
Solving a decimal word problem using a linear inequality with th...
Justin is choosing between two exercise routines.
In Routine \#1, he burns 25 calories walking. He then runs at a rate that burns 10.5 calories per minute.
In Routine \#2, he burns 46 calories walking. He then runs at a rate that burns 6.3 calories per minute.
For what amounts of time spent running will Routine \#1 burn fewer calories than Routine \#2?
Use $t$ for the number of minutes spent running, and solve your inequality for $t$.

Step 1 ：The problem is asking for the amount of time spent running where Routine #1 burns fewer calories than Routine #2. This can be represented as an inequality where the total calories burned in Routine #1 is less than the total calories burned in Routine #2.

Step 2 ：In Routine #1, Justin burns 25 calories walking and 10.5 calories per minute running. So, the total calories burned in Routine #1 can be represented as \(25 + 10.5t\).

Step 3 ：In Routine #2, Justin burns 46 calories walking and 6.3 calories per minute running. So, the total calories burned in Routine #2 can be represented as \(46 + 6.3t\).

Step 4 ：The inequality to solve is therefore \(25 + 10.5t < 46 + 6.3t\).

Step 5 ：Solving the inequality gives \(t < 5.0\). This means that for amounts of time spent running less than 5 minutes, Routine #1 will burn fewer calories than Routine #2.

Step 6 ：Final Answer: \(\boxed{t < 5.0}\)