Nora and Julia are both participating in a food eating tournament. They represent the number of hot dogs, h, each of them eats in t seconds in the equations shown. Use the equations to answer the question.
Nora’s equation:
t=4.8h
Julia's equation:
t=5.2h
For each of the following statements, decide whether it is true or false based on the information.
Statement
Nora eats faster than Julia does.
True Or False?
Julia eats faster than Nora does.
True Or False?
If Nora and Julia eat the same number of hot dogs, Julia will finish second.
True Or False?
If Nora and Julia eat the same number of hot dogs, Julia will finish first.
True Or False?
F, T, F, T
t,f,t,f
To answer these statements, we need to compare the values of t (time) in each equation.
Statement 1: Nora eats faster than Julia does.
To compare their eating speed, we need to compare the values of h (number of hot dogs) for the same amount of time. Let's set t=1 for comparison purposes.
For Nora: t = 4.8h,
For Julia: t = 5.2h.
Comparing the two equations at t=1, we see that Nora has a smaller value of h compared to Julia.
Therefore, Nora does not eat faster than Julia.
Statement 2: Julia eats faster than Nora does.
Using the same comparison as above, we can conclude that Julia eats faster than Nora because the value of h is greater in Julia's equation.
Statement 3: If Nora and Julia eat the same number of hot dogs, Julia will finish second.
This statement is false. If Nora and Julia eat the same number of hot dogs, that means they have the same value of h. However, since Julia eats faster (as stated in Statement 2), she will finish first, not second.
Statement 4: If Nora and Julia eat the same number of hot dogs, Julia will finish first.
This statement is true. As explained in Statement 3, if Nora and Julia eat the same number of hot dogs, Julia will finish first since she eats faster.
In summary:
Statement 1: False (Nora does not eat faster than Julia).
Statement 2: True (Julia eats faster than Nora).
Statement 3: False (Julia will finish first if they eat the same number of hot dogs).
Statement 4: True (Julia will finish first if they eat the same number of hot dogs).