Write and solve an inequality that represents the given situation.
If Lisa increased her rate by 15 mi/h, then in 2 hours she would travel a greater distance than she does in 3 hours at her present rate. What do you know about her present rate?
Just translate, if her present rate is x mph, then
2(x+15) > 3x
After I simplified I go:
2x+30>3x
30>x
So her present rate is less than 30 mi/h?
To represent this situation with an inequality, let's assume Lisa's present rate is denoted by "r" (in mi/h).
According to the problem, if Lisa increases her rate by 15 mi/h, she is traveling at a rate of (r + 15) mi/h. In 2 hours, she would travel a distance of 2(r + 15) miles.
On the other hand, if Lisa continues to travel at her present rate for 3 hours, she would cover a distance of 3r miles.
Since the problem states that the distance traveled in 2 hours at the increased rate is greater than the distance traveled in 3 hours at her present rate, we can write the following inequality:
2(r + 15) > 3r
Now, let's solve the inequality to determine what we know about Lisa's present rate:
2r + 30 > 3r
To isolate the variable, subtract 2r from both sides:
30 > r
The solution to this inequality is r < 30. Therefore, we know that Lisa's present rate must be less than 30 mi/h.