Save Work out the size of angle AED.
b) Work out x

x = 10°

Step-by-step explanation:

a). Since, opposite angles of a cyclic quadrilateral are supplementary angles"

   Therefore, in cyclic quadrilateral ABDE,

   m∠ABD + m∠AED = 180°

   110° + m∠AED = 180°

   m∠AED = 180° - 110°

                 = 70°

b). AD = ED [Given]

   m∠EAD = m∠AED [Since, opposite angles of equal sides are equal in measure]

   m∠EAD = m∠AED = 70°

   By triangle sum theorem in ΔABD,

   m∠BAD + m∠ABD + m∠ADB = 180°

   m∠BAD + 110° + 40° = 180°

   m∠BAD = 180 - 150

                 = 30°

    m∠AEB = m∠AED + m∠DAB [By angles addition postulate]

    m∠AEB = 70° + 30°          

                  = 100°

    By triangle sum theorem in the large triangle,

    x° + m∠AEB + m∠EAB = 180°

    x° + 100° + 70° = 180°

    x = 180 - 170

    x = 10°

First we need to write system of 2 equations with 2 variables:
x*6 + y*12.5 = 34
x+y = 3.5

for substitution we express one of variables in one of equations and put it in other equation.
x = 3.5-y

(3.5 - y)*6 + 12.5*y = 34
21 - 6y + 12.5y = 34
6.5y = 13
y = 2
x = 3.5 - y = 3.5 - 2 = 1.5

she ran for 1.5 hours and biked for 2 hours.
check:
1.5*6 + 2*12.5 = 9 + 25 = 34 = 34