Answer:
15 hours
Step-by-step explanation:
If it takes Frank 3 hours to assemble 7 bikes, we can find the rate at which he assembles bikes per hour.
Frank's rate is given by the ratio:
[tex] \textsf{Rate} = \dfrac{\textsf{Number of bikes}}{\textsf{Time}} [/tex]
So, Frank's rate is:
[tex] \textsf{Rate} = \dfrac{7 \, \textsf{bikes}}{3 \, \textsf{hours}} [/tex]
Now, we can find the rate per hour:
[tex] \textsf{Rate per hour} = \dfrac{7}{3} \, \textsf{bikes/hour} [/tex]
To find out how long it will take him to assemble 35 bikes, we can set up a proportion using the rate per hour:
[tex] \dfrac{\textsf{Number of bikes}}{\textsf{Time}} = \dfrac{\textsf{Rate per hour}}{1} [/tex]
Substitute the values:
[tex] \dfrac{35}{\textsf{Time}} = \dfrac{7}{3} [/tex]
Now, solve for the time ([tex]\textsf{Time}[/tex]):
[tex] \textsf{Time} = \dfrac{35 \times 3}{7} [/tex]
[tex] \textsf{Time} = \dfrac{105}{7} [/tex]
[tex] \textsf{Time} = 15 \, \textsf{hours} [/tex]
So, it will take Frank 15 hours to assemble the 35 bikes needed for the Christmas sale.
