Josh is choosing between two exercise routines.
In Routine #1, he does only running, burning 8.5 calories per minute.
In Routine #2, he burns 17 calories walking. He then runs at a rate that burns 4.25 calories per minute.
For what amounts of time spent running will Routine #1 burn at least as many calories as Routine #2?
Use t for the number of minutes spent running, and solve your inequality for t.
8.5t >= 17+4.25t
4.25t >= 17
t >= 4
To find the amount of time spent running when Routine #1 burns at least as many calories as Routine #2, let's set up an inequality.
In Routine #1, the number of calories burned is given by: 8.5t, where t is the number of minutes spent running.
In Routine #2, the number of calories burned from walking is constant at 17 calories. The number of calories burned from running is given by: 4.25t.
To compare these two routines, we need to set up the inequality:
8.5t ≥ 17 + 4.25t
Now, let's solve for t:
8.5t - 4.25t ≥ 17
4.25t ≥ 17
t ≥ 17/4.25
t ≥ 4
Therefore, the inequality is t ≥ 4. This means that if Josh spends at least 4 minutes running, Routine #1 will burn at least as many calories as Routine #2.
To solve this problem, we need to compare the calories burned in Routine #1 and Routine #2 and find the values of t (the number of minutes spent running) that satisfy the condition where Routine #1 burns at least as many calories as Routine #2. Let's go step by step.
In Routine #1, Josh only does running and burns 8.5 calories per minute. So, the total calories burned in Routine #1 can be calculated by multiplying the running time (t) with 8.5, which is 8.5t.
In Routine #2, Josh first walks and burns 17 calories per minute. Then, he runs at a rate that burns 4.25 calories per minute. Since we are interested in finding the total calories burned in Routine #2, we need to consider both walking and running. The calories burned from walking can be calculated by multiplying the walking time (let's call it w) with 17, which gives us 17w. The calories burned from running can be calculated by multiplying the running time (t) with 4.25, which gives us 4.25t. Therefore, the total calories burned in Routine #2 can be expressed as 17w + 4.25t.
Now, we can set up the inequality to find the values of t when Routine #1 burns at least as many calories as Routine #2:
8.5t ≥ 17w + 4.25t
To solve for t, let's isolate the term with t on one side:
8.5t - 4.25t ≥ 17w
Combine like terms:
4.25t ≥ 17w
Divide both sides by 4.25 to solve for t:
t ≥ (17/4.25)w
Simplifying the right side:
t ≥ 4w
So, any value of t that is greater than or equal to 4 times the walking time (w) will satisfy the condition where Routine #1 burns at least as many calories as Routine #2.