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13 (a) The ratio 20 minutes to 1 hour can be written in the form 1:n - OCR - GCSE Maths - Question 13 - 2017 - Paper 1
Question 13
13 (a) The ratio 20 minutes to 1 hour can be written in the form 1:n. Find the value of n. (b) The scale on a map is 1:25,000. How many kilometres on the ground ... show full transcript
Worked Solution & Example Answer:13 (a) The ratio 20 minutes to 1 hour can be written in the form 1:n - OCR - GCSE Maths - Question 13 - 2017 - Paper 1
Step 1
(a) Find the value of n.
Answer
To express the ratio of 20 minutes to 1 hour in the form 1:n, first, convert 1 hour into minutes:
1 hour = 60 minutes.
Now, the ratio can be set up as:
a : b = 20 : 60.
To simplify this ratio, divide both sides by 20:
a : b = 1 : 3.
Thus, we can conclude that the value of n is 3.
Step 2
(b) How many kilometres on the ground is represented by 6 cm on the map?
Answer
The map scale is given as 1:25,000, which means 1 cm on the map corresponds to 25,000 cm on the ground.
To find the distance represented by 6 cm on the map, we calculate:
Distance on ground = scale factor × map distance
Distance on ground = 25,000 cm/cm × 6 cm = 150,000 cm.
Now, convert centimeters to kilometers (since 100,000 cm = 1 km):
distance on ground in km = 150,000 cm ÷ 100,000 cm/km = 1.5 km.
Step 3