Please help with an inequality word problem!

Question

Tammy is choosing between two excercise routines. In Routine #1, she burns 20 calories walking. She then runs at a rate that burns 18.5 calories per minute. In Routine #2 , she burns 37 calories walking. She then runs at a rate that burns 14.25 calories per minute. For what amounts of time spent running will Routine #1 burn fewer than Routine #2? Use t for the number of minutes spent running.

a. Write an inequality to represent the above scenario.

b. Solve the inequality. Show your work.

c. Write your answer in a complete sentence.

Answer 1

a) 20 + 18.5t < 37 + 14.25t

b) 20 + 18.5t - 14.25t < 37 + 14.25t - 14.25t

20 + 4.25t < 37

20 - 20 + 4.25t < 37 - 20

4.25t < 17

4.25t/4.25 < 17/4.25

t < 4

c) If Tammy runs for less than 4 minutes, routine #1 will burn fewer calories than routine #2.

Answer 2

Say that t equals the number of minutes exercised.

Routine #1: y₁ = 20 + 18.5t Routing #2: y₂ = 37 + 14.25t

They want to know the amount of time running will make Routine #1 burn fewer than Routine #2, in other words, the inequality Routine #1 < Routine #2, which you can represent this way:

y₁ < y₂

or

20 + 18.5t < 37 + 14.25t Then you want to solve for t:

18.5t < 17 + 14.25t Subtract 20 from both sides

4.25t < 17 Subtract 14.25t from both sides

t < 4 Divide both sides by 4.25

for a. the inequality is 20 + 18.5t < 37 + 14.25t

for b. the solution is t < 4 (work shown above)

for c., putting your solution into words, For any time less than four minutes, Routine #1 will result in burning fewer calories than Routine #2. (At four minutes, you will burn the same amount of calories in both routines, and any more than four minutes, Routine #2 will burn more calories.)