Taxi fare is $1.20 for the first 1/4 mile and $0.10 for each additional 1/8 mile. A man pays a fare of $3.00. The number of miles he has traveled is:

0.10 per 1/8 mile = 0.8 per mile

miles = m

(m - 1/4 ).10 = 3.00 - 1.20

thanks sir!

(m-1/4)(.8) = 3 - 1.2

2 1/2

To find the number of miles the man has traveled, we need to determine how many additional 1/8 miles he traveled after the first 1/4 mile.

Let's start by finding the cost of the additional miles. The fare for each additional 1/8 mile is $0.10.

Since 1 mile is equal to 8 (1/8 mile) segments, we can divide the cost of each additional 1/8 mile by 8 to get the cost per mile.

Cost per mile = $0.10 / 8 = $0.0125

Now, we can subtract the cost of the first 1/4 mile from the total fare to get the cost of the additional miles.

Cost of additional miles = Total fare - Cost of first 1/4 mile = $3.00 - $1.20 = $1.80

To find the number of additional miles traveled, we can divide the cost of additional miles by the cost per mile.

Number of additional miles = Cost of additional miles / Cost per mile = $1.80 / $0.0125 = 144

However, we need to add the initial 1/4 mile to the total number of miles traveled.

Total miles traveled = Number of additional miles + 1/4 mile = 144 + 1/4 = 144.25 miles

Therefore, the man has traveled 144.25 miles.