bob and nina make dog leashes. bob can make 7 leashes in 2 hours and nina can make 4 leashes in 1 hour…

bob and nina make dog leashes. bob can make 7 leashes in 2 hours and nina can make 4 leashes in 1 hour. enter an equation that can be used to find the number of hours, t, it takes bob and nina to make 60 leashes together. enter your response in the first response box. enter the number of hours, t, it takes bob and nina to make 60 leashes together. enter your response in the second response box.
Answer
Explanation:
Step1: Find Bob's rate
Bob makes 7 leashes in 2 hours, so his rate is $\frac{7}{2}$ leashes per hour.
Step2: Find Nina's rate
Nina makes 4 leashes in 1 hour, so her rate is 4 leashes per hour.
Step3: Set up the equation
The combined rate of Bob and Nina is $\frac{7}{2}+4$ leashes per hour. In $t$ hours, they make 60 leashes. So the equation is $(\frac{7}{2}+4)t = 60$.
Step4: Simplify the left - hand side
$\frac{7}{2}+4=\frac{7 + 8}{2}=\frac{15}{2}$. The equation becomes $\frac{15}{2}t=60$.
Step5: Solve for $t$
Multiply both sides by $\frac{2}{15}$, so $t = 60\times\frac{2}{15}=8$.
Answer:
Equation: $(\frac{7}{2}+4)t = 60$ Number of hours: 8