Eagle Electric Bikes charges its customers a per-minute fee for bike rentals. The first time Ross rented from them, he got a $10 new-customer discount and used the bike for 64 minutes. The second time, he used the bike for 39 minutes. He noticed that he was charged the same amount each time.

Question

What is the per-minute fee to rent an electric bike?
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Answer 1

Let the per-minute rental fee be denoted as $x$.

For Ross's first rental:

• The time he used the bike is 64 minutes.
• He received a $10 new-customer discount.

Thus, the cost for the first rental can be expressed as: $${\text{Cost}}_1=64x-10$$

For Ross's second rental:

• The time he used the bike is 39 minutes.

The cost for the second rental is: $${\text{Cost}}_2=39x$$

Given that Ross was charged the same amount for both rentals, we set the costs equal: $$64x-10=39x$$

To solve for $x$, we first rearrange the equation: $$64x-39x=10$$ $$25x=10$$ Now divide both sides by 25: $$x=\frac{10}{25}=\frac{2}{5}=0.4$$

Therefore, the per-minute fee to rent an electric bike is: $$\boxed{{\displaystyle 0.4}}$$

To verify, we can calculate both costs using $x=0.4$.

For the first rental: $${\text{Cost}}_1=64(0.4)-10=25.6-10=15.6$$

For the second rental: $${\text{Cost}}_2=39(0.4)=15.6$$

Both costs are equal, confirming that the per-minute fee is indeed: $$\boxed{{\displaystyle 0.4}}$$