Let's denote the distance Eloise and Christian traveled as D (in miles).
Eloise traveled at a speed of 15 mph, so her time (T1) can be calculated using the formula:
T1 = D / 15
Christian traveled at 30 mph, and his time (T2) was 3 hours less than Eloise's time:
T2 = T1 - 3
Now, we can substitute the expression for T1 from the first equation into the second equation:
T2 = (D / 15) - 3
We know that time (T) is equal to distance (D) divided by speed (S):
T = D / S
So, we can rewrite the equations for T1 and T2 using the formula for time:
T1 = D / 15
T2 = D / 30
Now, let's substitute T1 and T2 back into the equation T2 = (D / 15) - 3:
(D / 30) = (D / 15) - 3
Now, let's solve for D:
(D / 30) - (D / 15) = 3
To subtract the fractions, we need a common denominator, which is 30:
(2D / 30) - (D / 30) = 3
Now, combine the fractions:
(D / 30) = 3
Now, multiply both sides of the equation by 30 to isolate D:
D = 3 * 30
D = 90
So, Eloise and Christian traveled a distance of 90 miles.