Questions

1. A van travelled from Kitale to Kisumu a distance of 160km. The average speed of the van for the first 100km was 40km/h and the remaining part of the journey its average speed was 30km/h. Calculate the average speed for the whole journey. (3 mks)
2. A watch which looses a half-minute every hour was set to read the correct time at 0545h on Monday. Determine the time, in the 12 hour system, the watch will show on the following Friday at 1945h.
3. A watch which loses a half-minute every hour was set to read the correct time at 0445h on Monday. Determine the time in 12-hour system, the watch will show on the following
   Friday at 1845h
4. The timetable below shows the departure and arrival time for a bus plying between two towns M and R, 300km apart
   

   Town	Arrival	Departure
   M		0830h
   N	1000h	1020h
   P	1310h	1340h
   Q	1510h	1520h
   R	1600h

   1. How long does the bus take to travel from town M to R?
   2. What is the average speed for the whole journey?

Answers

1. Average speed = ^{Total distance travelled}/_{total time taken}
   Time taken = ¹⁰⁰/₄₀ + ^{(160 −100)}/₃₀
   = 2½ + 2 = 4½
   Total distance = 160 km
   Average speed = ¹⁶⁰/_4½
   = 35.56 km/h
2. Time between Monday 0545hr and Friday 1945
   = 4x 24 + 14 = 110 hrs
   Time lost = 0.5 x 110 = 55 min.
   Time in 12 hr system
   (1945 – 55 – 1200)
   = 6.50 p.m.
3. Time between Monday 0445h and Friday 1845h
   = 4 x 24 + 14 = 110h
   Time lost = 0.5 x 110
   = 55min
   Time shown in 12 hour system
   1845 – 55 = 1750 h
   = 5.50 p.m
4.  
   1. 1600h – 830h = 7hrs 30min or 7 ½ hours
   2. Average speed = ³⁰⁰/_7½ = 40km/h