Let the number of miles driven in a day be represented by $x$.

For Company A:

• Daily cost: $100
• Per mile cost: $0.30

Thus, the total cost for Company A is: $C_A = 100 + 0.30x$

For Company B:

• Daily cost: $20
• Per mile cost: $0.70

Thus, the total cost for Company B is: $C_B = 20 + 0.70x$

To find the number of miles at which the costs are the same, we set the two equations equal to each other: $100 + 0.30x = 20 + 0.70x$

Now, solve for $x$:

1. Subtract $20$ from both sides: $100 - 20 + 0.30x = 0.70x$ $80 + 0.30x = 0.70x$

2. Subtract $0.30x$ from both sides: $80 = 0.40x$

3. Divide both sides by $0.40$: $x = \frac{80}{0.40} = 200$

Thus, the number of miles at which the rental costs are the same is $\boxed{200}$ miles.

Would you like further explanation on this, or do you have any questions?

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Here are 5 related questions you might find helpful:

1. How would the costs compare if you drive fewer than 200 miles?
2. What if Company B also added a surcharge after a certain number of miles?
3. How would you model the costs if you rented the truck for multiple days?
4. What if Company A offered a discount for miles over 300 in a day?
5. Can you find the breakeven point if both companies charge per hour instead of per mile?

Tip: When solving problems involving comparisons between two linear equations, always look for where the equations intersect to find the breakeven point!