Question

Eloise made the trip on Sunday, and Christian made the same trip on Monday. Eloise traveled at 15 mph. Christian traveled at 30 mph, so his time was 3 hours less than Eloise's time. How far did they travel?

Answer 1

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.