Respuesta :
Answer:
Amanda will catch up Ben after 0.6 hours.
Step-by-step explanation:
Amanda begins jogging along the same path at 7 mi/h.
This means that Amanda's position, after t hours, is given by:
[tex]A(t) = 7t[/tex]
Ben starts walking along a path at 2 mi/h.
Amanda leaves after one and a half hour, which means that Ben will be at position 2*1.5 = 3. So Ben's position after t hours is given by:
[tex]B(t) = 3 + 2t[/tex]
How long (in hours) will it be before Amanda catches up to Ben?
This will happen when:
[tex]A(t) = B(t)[/tex]
So
[tex]7t = 3 + 2t[/tex]
[tex]5t = 3[/tex]
[tex]t = \frac{3}{5}[/tex]
[tex]t = 0.6[/tex]
Amanda will catch up Ben after 0.6 hours.
It would take Amanda 0.6 hours or 6/10 hours to catch up with Ben.
This question comes from a topic in mathematics called rates and it's used to compare two values with each other and how one value affects the other value.
Let s represent the distance Amanda travels until she meet Ben.
We can set a timer on our phone when she leaves in order to track the time taken.
Let t represent the time taken.
Set of Equation
We can come up with two equations from these scenario
- d - 3 = 2t------ equation (i)
- d = 7t ----- equation (ii)
Substitute equation (ii) into equation (i)
[tex]7t -3 =2t[/tex]
collect like terms
[tex]7t-2t=3\\5t=3\\t=3/5\\t=0.6[/tex]
From the above, we can see it took her 0.6 hours to catch up with Ben.
Learn more about rates here;
https://brainly.com/question/14323743
