Tsela flew by plane from Lesotho to Nigeria.
The flight time was 6 hours 42 minutes.
The flight leaves Lesotho at 8.27 pm on Monday.
(a) On what day, and at which time does the plane arrive in Nigeria.

(b) The average speed of the plane is 650 kilometres per hour.
Calculate the distance the plane flew.

(c) The return journey took 30 minutes less.
Find the average speed of the plane for the return journey.

The table shows arrival time, lunch time, and departure time for three employees Chale, Mpata and Nko.

EMPLOYEE	ARRIVAL TIME	LUNCH TIME	DEPARTURE TIME
Chale	08 00 hrs	12 30 hrs – 13 30 hrs	16 45 hrs
Mpata	10 05 hrs	13 15 hrs – 14 00 hrs	17 05 hrs
Nko	07 30 hrs	12 05 hrs – 13 05 hrs	17 20 hrs

(a) Write Nko's time in 12 hour clock.

(b) Another employee, Thipa, takes 3 hours 5 minutes at work before lunch.
Between Thipa and Mpata, who spends the longest time at work before lunch?
Support your answer.

(c) One day Mpata took his lunch outside the workplace.
Calculate the time, in hours and minutes, that Mpata spent at work on this day.

(d) The distance, d km, between Chale's home and work is 120 km, correct to the nearest 10 km.
(i) Complete the statement for d km.

(ii) One day after work Chale reached home at 18 25 hrs.
Calculate the upper bound to his average speed in this journey.

The diagram shows the positions of three places; Home (H), School (S) and Union hall (U).
HS = 230 km, HU = 157 km and angle SHU = 46°. (a) Show that the distance US is approximately 165 km.

(b) Calculate the shortest distance from Union hall (U) to the road HS.

(c) Ts'itso leaves School at 1645hrs and travels at an average speed of 50 km/h.
Calculate the time he arrives at Home.

A firm produces door frames and window frames.
For one order the firm has 100 hours available to assemble the frames and 150 hours available to polish them.

	Time in hours to produce one unit
	Door frames	Window frames	Time available (h)
Assembling	1	4	100
Polishing	3	2	150

Let d be the number of door frames produced and w be the number of window frames produced.

(a) Write an expression, in terms of d and w, for the total number of hours needed to assemble the door frames and window frames.

(b) Two inequalities that represent the information in the table are:
$3d+2w\le 150$ and $w\ge 0$.
Write the other two inequalities.

(c) On the grid provided, show the information from part (b) by drawing 4 straight lines and shading the region that is not required.

(d) Given that the firm makes a profit, P in Maloti, where $P=500d+700w$, use your graph to find the maximum profit the firm can make.

Three students, Atang, Bene and Chabeli, train daily for one week for a marathon race.
The table shows the average running and cycling speeds of the students during training.

Student	Running (km/h)	Cycling (km/h)
Atang	2.5	3
Bene	3	2.5
Chabeli	3.8	3

Each student, runs for 1 hour and cycles for 1 hour in total during weekdays, and runs for 3 hours and cycles for 2 hours in total during weekends.

(a) Write the training speed in a matrix form.

(b) The total time training is represented by the matrix $B=\left(\begin{array}{cc}1& 3\\ 1& 2\end{array}\right)$.
(i) Work out AB.

(ii) Explain what AB represents.

(iii) Find the total distance travelled in training by each student during the week.

Lineo runs at a rate of 170 m/min and walks at a rate of 90 m/min.
Lineo leaves home and takes 6 minutes, by running and walking, to reach a bus stop.
Lineo runs for t minutes.

(i) Find, in terms of t, an expression for:
(a) the number of minutes she walks,

(b) the distance she runs,

(c) the distance to the bus stop.

(ii) The distance to the bus stop is 740 m.
Find the value of t.