To attend a family reunion, Beth drives 100 mi from Fresno and Clara drives 220 mi from San Jose. Both women drive the same speed in miles per hour, but Clara's drive takes 2 hours longer than Beth's. Find the length of Beth's drive.

a. 1 hour. b. 2.2 hours
c. 1.66 hours d. 3.66 hours

Beth: t hours.

Clara:(t+2) Hours.

Eq1: r*t = 100 mi

Eq2: r*(t+2) = 220 mi.
r*t + 2r = 220
Replace r*t with 100:
100 + 2r = 220
2r = 120
r = 60 mi./h.

In Eq1, replace r with 60:
60t = 100
t = 1.66 Hours. = Beth's driving time.

To solve this problem, we can use the formula Distance = Speed * Time.

Let's assume that the speed at which both Beth and Clara drive is 's' (miles per hour).

According to the given information, Beth drives 100 miles and Clara drives 220 miles.

Using the formula, we can set up the following equations:

100 = s * t1 -- (Equation 1)
220 = s * t2 -- (Equation 2)

We are also given that Clara's drive takes 2 hours longer than Beth's drive. So, we can write:

t2 = t1 + 2 -- (Equation 3)

To find the length of Beth's drive (t1), we need to solve this system of equations.

Let's solve the equations:

From Equation 1, we can express t1 in terms of s:

t1 = 100 / s

Now we substitute this value of t1 in Equation 3:

t2 = t1 + 2
t2 = (100 / s) + 2 -- (Equation 4)

We can substitute the value of t2 from Equation 2 in Equation 4:

220 = s * t2
220 = s * ((100 / s) + 2)
220 = 100 + 2s

Rearranging the equation:

2s = 220 - 100
2s = 120
s = 120 / 2
s = 60

Now we substitute this value of s in Equation 1 to find t1:

100 = s * t1
100 = 60 * t1
t1 = 100 / 60
t1 = 1.66 hours

Therefore, the length of Beth's drive is 1.66 hours.

Hence, the correct answer is option c. 1.66 hours.