WELCOME TO THIS PAGE INTENDED FOR STUDENTS AT THE UNIVERSITY OF THE WESTERN CAPE REGISTERED FOR THE MODULE QSF 131:
W6 L3
TEST DATES
CLASS re-TEST 2 |
WED, 10 MARCH |
B1 LUNCH-TIME |
TUTORIAL TEST 3 |
THURS, 11 MARCH |
B2 LUNCH-TIME |
W6 L3
A. CLASS RE-TEST 2 : 10 MARCH 2010
A taxi-fleet owner of a number of similar 1600 cc four-door sedans, charges the following weekly rates for transport services:
· R12 for every kilometer travelled; and
· R20 basic fee per half an hour of travelling.
· In addition to the above, the charge for waiting is R48 per hour. Over weekends his fee is 25% more than his weekly rate.
3.1 Calculate his gross income for a 5-day week, if his fleet carried passengers for a total of 2450 kilometers in 500 hours. The total waiting time during that week was 36 hours.
3.2 If petrol costs him R7.45 per liter, which allows him to travel 8 km on the average, how much petrol did he use during the week when he covered 2450 kilometers;
3.3 How much is his gross income for a weekend during which he conveyed passengers over 1450 km in 240 hours with a waiting time of 24 hours?
3.4 If his weekly fleet maintenance bill amounts to R2000, and the wages of the drivers total R 10 000, calculate his loss/profit for the week, using your answers in 3.1 and 3.2 above for the owner’s gross income and petrol costs.
CAR MAGAZINE JANUARY 2001
A.
11.25 litres / 100 km: 2.5 litre car
THIS IMPLIES:
50% MORE, or
33 LESS
The ANSWER depends on the angle from which you are looking.
CALCULATION:
CHANGING FROM FIAT:
CHANGING TO FIAT:
B. COURSE READER: pp.103 – 105 : PERCENTAGES!!!
RATIOS/RATES
PROBLEM 1
In the recent 2008 Olympic games held in the Bird’s Nest stadium in Beijing, the Jamaican sprinter Usain Bolt ran the 100 metres in 9.69 seconds to clinch the gold medal for this event.
(a) Estimate his average speed over this distance in km per hour.
(b) Express his average speed over this distance in km per hour.
Solution
(a) One has a good idea of 20, 60 and 80 km/hour (stemming from our car driving experiences). Hence as good estimate would be 30-40 km/hr.
(b) Time needed to cover 100 metres = 9.69 seconds
Since 1 km is ten times 100 metres, time taken to complete 1 km = 96.9 seconds = 1.615 minutes
(divide by 60, since 60 secs = 1 minute)
Therefore, the distance covered in 1 hour = 60 divided by 1.615 = 37.15 km
Therefore Bolt’s average speed = 37.15 km/hour
WHICH IS BETTER?
PROBLEM 2
A special type of engine oil treatment is sold for R119 for 350 ml at a particular store. The same store also sells a 500 ml container of the same thing for R149. Which is the better buy?
Partial Solution:
Work out the respective prices per ml for each OR
Work out the respective quantities per rand.
DO YOURSELF
In the World Athletics Championship competition held in BERLIN, Germany on Sunday 16 August 2009, the Jamaican sprinter Usain Bolt ran the 100 metres in 9.58 seconds to clinch the gold medal for this event. Determine:
(1) By how many seconds did Bolt improve his previous world record set a year ago? (0.11 secs)
(2) His speed in km/h over the distance. (37.5782881 km/h)
(3) What is the percentage decrease in the time over the distance? (1.135%)
(4) What is the percentage increase in his speed over this distance? (1.152%)
PROBLEM 4
At the World Athletics Championships held in Berlin, Germany, in August 2009, the South African athlete Caster Semenye ran the 800 metres in 1 minute 55.45 seconds to clinch the gold medal for this event.
4.1 Calculate her average speed in km/h over the 800m distance.
4.2 Assuming the unlikely that Caster ran at the same average speed calculated in 10.1 above, what would her average time over 100 metres be?
PROBLEM 5
SOCCER
If a world class soccer player (RONALDO) on the average covers 100 metres every 54 seconds, what is his average speed in :
(a) m/sec
(b) km/hr
How much slower is this speed than (c) Bolt’ s (d) Semenya’s (which is an unlikely comparison for obvious reasons!!)
© DESMOND DESAI, DMD EDU-HOME, 2010
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