Question 15

Explanation

We start by defining variables for speed and time. Let $v_1$ be the speed of the first car, so the speed of the second car is $v_2 = v_1 + 15$. We know the difference in their travel times is 1 hour.

Since time is distance divided by speed ($t = \frac{s}{v}$), we can set up an equation based on this time difference:

Next, we solve this equation to find $v_1$. Multiply both sides by $v_1(v_1 + 15)$ to eliminate the denominators:

We factor the quadratic equation:

Since speed cannot be negative, we take $v_1 = 75$ km/h. Thus, the speed of the second car is:

Finally, we calculate the average speed of the two cars: