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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 (Easy)

Solving problems is about working things out. You learn maths at school because it is an important academic subject, but the maths you learn also has a lot of practical applications.

Let's say you wanted to decorate your bedroom. How many rolls of wallpaper will you need? You could guess, but that could be a waste of money - or worse having to go back to the shop halfway through decorating to get some more.

How about going to visit your friend who has moved to another part of the country. They want to know at roughly what time you will arrive. Your journey is 250 miles by car and is mostly motorway. Do you make a rough guess? You might turn up far too early, or far too late. How do you work it out?

Do this 11-plus quiz and improve your knowledge of maths to solve real life problems.

1 .

Helen's car does 45 miles to the gallon. How many gallons (gal) of petrol 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

2 .

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?

600

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

3 .

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!

4 .

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

5 .

In how many ways can the letters ABC be arranged if you can only arrange two letters at a time, e.g. AB?

Here are the six arrangements:
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

6 .

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

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

7 .

1 mile = 1.61 km. What would a distance of 30 miles be in kilometres?

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

8 .

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

9 .

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

&frac18; 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

10 .

Rick is driving his sports car at 70 mph (miles per hour), and he is travelling 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

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)