Two business partners, Alex and Morgan, jointly lease a warehouse facility. Alex stores 20 shipping containers in the space for 5 months. Morgan uses the facility to store 30 freight crates for 5 months and 40 cargo pallets for 3 months. In terms of floor space consumption, 2 shipping containers take up the same space as 5 freight crates, and 3 freight crates equal 6 cargo pallets. What portion of the total rental expense should Alex cover?

The correct option is $\frac{25}{46}$.

To determine what portion of the total rental expense Alex should cover, we need to calculate the space-time usage (floor space consumed multiplied by months stored) for both Alex and Morgan in terms of a common unit.

Step 1: Determine the conversion ratios between space units.
Let us represent:
- C = space of 1 shipping container
- F = space of 1 freight crate
- P = space of 1 cargo pallet

From the given relationships:
1. "2 shipping containers take up the same space as 5 freight crates":

$2C=5F\Rightarrow C=\frac{5}{2}F=2.5F$

2. "3 freight crates equal 6 cargo pallets":

$3F=6P\Rightarrow F=2P\Rightarrow P=0.5F$

We will express all space units in terms of freight crates (F):
- 1 shipping container = 2.5 freight crates
- 1 freight crate = 1 freight crate
- 1 cargo pallet = 0.5 freight crates

Step 2: Calculate Alex's total usage (in Freight Crate-Months).
Alex stores 20 shipping containers for 5 months.

$\text{Alex's Space}=20\times 2.5F=50F$

$\text{Alex's Usage}=50F\times 5\text{months}=250\text{freight crate-months}$

Step 3: Calculate Morgan's total usage (in Freight Crate-Months).
Morgan has two sets of stored items:
1. 30 freight crates for 5 months:

$30F\times 5\text{months}=150\text{freight crate-months}$

2. 40 cargo pallets for 3 months:

$\text{Space for 40 pallets}=40\times 0.5F=20F$

$\text{Usage for pallets}=20F\times 3\text{months}=60\text{freight crate-months}$

$\text{Morgan's Total Usage}=150+60=210\text{freight crate-months}$

Step 4: Calculate Alex's share of the total rental expense.

$\text{Total Facility Usage}=250+210=460\text{freight crate-months}$

$\text{Alex's Portion}=\frac{250}{460}=\frac{25}{46}$

Therefore, Alex should cover $\frac{25}{46}$ of the total rental expense.