On a map 3/6 inch represents 60 kilometers. Distance A to B is 4 5/8 inches. Distance C to D is 5 3/5 inches. Distance E to F is 9 5/6 inches.
What is the number of kilometers between A and B?
What is the number of kilometers between C and D?
What is the distance between E and F?
If Jack has to travel from point A to F, what is the total map distance and the actual kilometers he will cover?
A to B: Since the scale does not change,
60/(3/4) = x/(4 5/8)
60*4/3 = x * 37/8
x = 60 * 4/3 * 8/37
Do the other parts the same way.
Remember that the scale does not change! If a distance is twice a big on the map, it is twice as big in the world.
To find the number of kilometers represented by a given length on the map, we can set up a proportion. The given information tells us that 3/6 inch represents 60 kilometers. We can now set up the proportion:
(3/6 inch) / (60 kilometers) = (4 5/8 inches) / (x kilometers)
Cross-multiplying, we get:
(3/6) * x = (4 5/8) * 60
To simplify the right side of the equation, we need to convert 4 5/8 inches to a mixed number or improper fraction. In this case, we'll convert it to an improper fraction:
(4 5/8) = ((4 * 8) + 5) / 8 = 37/8
Now our equation becomes:
(3/6) * x = (37/8) * 60
To solve for x, we can cancel out the common factor of 3 in the numerator and denominator of the left side:
1/2 * x = (37/8) * 60
Multiplying the fractions:
1/2 * x = 2220/8
To isolate x, we multiply both sides by 2/1:
x = (2220/8) * (2/1)
Simplifying the fraction:
x = 1110/1
Therefore, the number of kilometers between A and B is 1110 kilometers.
Repeating the same process, we can find the number of kilometers between C and D:
(3/6 inch) / (60 kilometers) = (5 3/5 inches) / (x kilometers)
Converting 5 3/5 inches to an improper fraction:
(5 3/5) = ((5 * 5) + 3) / 5 = 28/5
The equation becomes:
(3/6) * x = (28/5) * 60
Canceling out the common factor of 3:
1/2 * x = (28/5) * 60
Multiplying the fractions:
1/2 * x = 1680/5
Isolating x by multiplying both sides by 2/1:
x = (1680/5) * (2/1)
Simplifying the fraction:
x = 3360/5
Therefore, the number of kilometers between C and D is 672 kilometers.
For the distance between E and F, we can follow the same steps:
(3/6 inch) / (60 kilometers) = (9 5/6 inches) / (x kilometers)
Converting 9 5/6 inches to an improper fraction:
(9 5/6) = ((9 * 6) + 5) / 6 = 59/6
The equation becomes:
(3/6) * x = (59/6) * 60
Canceling the common factor of 3:
1/2 * x = (59/6) * 20
Multiplying the fractions:
1/2 * x = 590/6
Isolating x by multiplying both sides by 2/1:
x = (590/6) * (2/1)
Simplifying the fraction:
x = 590/3
Therefore, the distance between E and F is approximately 196.67 kilometers.
To find the total map distance and actual kilometers Jack will cover from point A to F, we add the distances between A to B, B to C, C to D, and D to F:
Distance from A to B: 4 5/8 inches
Distance from C to D: 5 3/5 inches
Distance from E to F: 9 5/6 inches
Total map distance: (4 5/8) + (5 3/5) + (9 5/6) = 18 4/24 inches
To find the actual kilometers covered by Jack, we can set up the proportion:
(3/6 inch) / (60 kilometers) = (18 4/24 inches) / (x kilometers)
Converting 18 4/24 inches to an improper fraction:
(18 4/24) = ((18 * 24) + 4) / 24 = 436/24
The equation becomes:
(3/6) * x = (436/24) * 60
Canceling the common factor of 6:
1/2 * x = (436/24) * 10
Multiplying the fractions:
1/2 * x = 2180/24
Isolating x by multiplying both sides by 2/1:
x = (2180/24) * (2/1)
Simplifying the fraction:
x = 2180/12
Therefore, the actual kilometers Jack will cover from point A to F is approximately 181.67 kilometers.