Question

Renting a bike requires a security deposit of $\$30$ and costs an additional $\$2$ per hour. If Robert has $\$42$, what is the maximum duration (in hours) for which he can rent a bike?

• A. 5.5 h
• B. 4 h
• C. 6 h
• D. 6.5 h

Answer 1

The correct option is C 6 h

Security deposit $=\$30$
Additional cost per hour $=\$2$
Robert's budget $=\$42$

Let the maximum duration for which Robert can rent a bike be $t$ h.

For $t$ h: Security deposit + cost per hour $\times$ $t$ $\le$ Robert's budget
$\Rightarrow 30+2\times t\le 42\Rightarrow 2\times t\le 42-30\Rightarrow 2\times t\le 12\Rightarrow t\le \frac{12}{2}\Rightarrow t\le 6h$
Hence, Robert can rent a bike for a maximum of 6 h.