Mary Baker rides a bicycle and travels at twice the speed of Wayne Siegert. Mary and Wayne begin a race at the same time and after 4 hours, Mary is 36 miles ahead of Wayne. a) What is Wayne's speed? b) What is Mary's speed? a) The speed of Wayne is \( \square \) miles per hour. (Type an integer or a decimal.)

To solve this problem, let Wayne's speed be \( x \) miles per hour. Since Mary rides at twice Wayne's speed, her speed would be \( 2x \) miles per hour. In 4 hours, Mary travels: \[ 2x \times 4 = 8x \] miles. Meanwhile, Wayne travels: \[ x \times 4 = 4x \] miles. According to the problem, Mary's distance is 36 miles ahead of Wayne's after 4 hours. Therefore, we can set up the equation: \[ 8x - 4x = 36 \] \[ 4x = 36 \] \[ x = 9 \] Thus, Wayne's speed is \( 9 \) miles per hour. For Mary's speed: \[ 2x = 2 \times 9 = 18 \] miles per hour. So, the final speeds are: - Wayne's speed: \( 9 \) miles per hour. - Mary's speed: \( 18 \) miles per hour. a) The speed of Wayne is \( 9 \) miles per hour. b) The speed of Mary is \( 18 \) miles per hour.