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If it takes 1 man 2 days to paint a fence, how long will it take 4 men, working at the same speed, to paint the same fence?
Solving Problems 2
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Solving problems is about working things out. You learn math at school because it is an important academic subject, but the math you learn also has a lot of practical applications.
1 .
In how many ways can the letters ABC be arranged if you can only arrange two letters at a time, e.g. AB?
4
8
3
6
2 .
A fathom is used for measuring the depth of water: 1 fathom = 6 feet or 1.83 m. How many fathoms is 1,830 m?
10,000
10
1,000
100
1,830 m = 1,830 ÷ 1.83 = 1,000 fathoms. You have to divide by 1.83 because you want to find out how many 'lots' of 1.83 there are in 1,830 : each 'lot' equals 1 fathom: this is the same as adding 'lots' of 1.83 to itself until you get to 1,830
3 .
If it takes 1 man 2 days to paint a fence, how long will it take 4 men, working at the same speed, to paint the same fence?
½ day
8 days
¼ day
⅛ day
It will take 4 men 2 ÷ 4 = ½ day. You have to divide by 4 because you want to find out how many 'lots' of 4 there are in 2: each 'lot' equals 1 day. Think of it like this: there are four times as many people working, so the job is going to take a quarter of the time it took one man to do the job
4 .
A number of 100 m long pieces of material are hung up separately to dry in a large open area. If it takes 4 hours for a single piece of material to dry, how long will it take for 250 pieces to dry?
1,000 hr
4 hr
10 hr
62.5 hr
Did you get caught out here? They will ALL have dried in 4 hours: there is NO relationship between the number of pieces and the drying time. D'oh!
5 .
A crane can lift a maximum load of 15,000 kg. How many boxes each weighing 250 kg can be loaded into a container for the crane to lift?
6
600
60
150
The number of boxes = 15,000 ÷ 250 = 60. You have to divide by 250 because you want to find out how many 'lots' of 250 there are in 15,000: each 'lot' equals 1 box: this is the same as adding 'lots' of 250 to itself until you get to 15,000
6 .
Henry's house is four times bigger than Charlie's house. If Henry's house is 1,000 m2, what is the size of Charlie's house?
250 m2
4,000 m2
2,500 m2
25 m2
Charlie's house is one-quarter of the size of Henry's house = 1,000 ÷ 4 = 250 m2. Multiplying by ¼ is the same as dividing by 4. The same applies for similar fractions
7 .
In order for the machine to operate, the knob has to be turned clockwise through a quarter of a turn. How many degrees are there in a quarter of a turn?
45°
180°
90°
270°
A quarter of a turn is one-quarter of 360°: just divide 360° by 4
8 .
1 mile = 1.61 km. What would a distance of 30 miles be in kilometers?
19 km
84 km
48 km
20 km
If 1 mile = 1.61 km, then 30 miles will be 30 times 1.61 because 30 miles is 30 times more than 1 mile: 30 × 1.61 = 48.3 km
9 .
Rick is driving his sports car at 70 mph (miles per hour), and he is traveling from London to Lincoln on the M1: a distance of about 140 miles. If he maintains this speed, how long will it take him to get to Lincoln?
2 hr
½ hr
20 hr
0.2 hr
It will take him 140 ÷ 70 = 2 hr. You have to divide by 70 because you want to find out how many 'lots' of 70 there are in 140: each 'lot' equals 1 hour
10 .
Helen's car does 45 miles to the gallon. How many gallons (gal) of gasoline will she need for a 315 mile journey?
70 gal
7 gal
0.7 gal
6 gal
For a 315 mile journey she will need 315 ÷ 45 = 7 gal. You have to divide by 45 because you want to find out how many 'lots' of 45 there are in 315: each 'lot' equals 1 gallon: this is the same as adding 'lots' of 45 to itself until you get to 315
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AB
AC
BA
BC
CA
CB
With problems like this, work in a column because it's easier to see what you are doing. Look at the columns carefully, and you should get an idea of how to deal with simple arrangements like this