To find Mr. Valenzuela's average speed during the last 1 1/4 hours (which is 1.25 hours), we need to first determine how many miles he has driven in the first 2 hours and how many miles remain to be covered in the total journey of 180 miles.
- Distance driven in the first 3/4 hour: 48 miles
- Distance driven in the next hour: 52 miles
Now we calculate the total distance covered in the first 1 3/4 hours (1 hour and 45 minutes):
\[ \text{Total distance in the first 1 3/4 hours} = 48 \text{ miles} + 52 \text{ miles} = 100 \text{ miles} \]
Now, we subtract this distance from the total distance of 180 miles to find out how far he needs to drive in the last 1 1/4 hours:
\[ \text{Distance remaining} = 180 \text{ miles} - 100 \text{ miles} = 80 \text{ miles} \]
Next, we need to calculate the average speed during that last 1 1/4 hours:
\[ \text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{80 \text{ miles}}{1.25 \text{ hours}} \]
Calculating that gives:
\[ \text{Average speed} = 80 \div 1.25 = 64 \text{ mph} \]
Thus, Mr. Valenzuela's average speed in the last 1 1/4 hours is 64 miles per hour (mph).