Mathematics

Problem

A car travels from town

A

to town

B

, a distance of

75\,\text{km}

, at a uniform speed of

v\,\text{km/h}

. After staying in town

B

for

15\,\text{min}

, it returns to

A

at a uniform speed of

60\,\text{km/h}

. The whole trip, including the halt at

B

, takes exactly

3\,\text{h}

. a. (i) Write an equation in

v

representing the total time for the journey. b. (ii) Solve the equation to find the value of

v

. c. (iii) Calculate the total distance travelled by the car. d. (iv) Determine the average speed for the entire trip, including the halt at

B