Question

3 roads, a, b, and
c. b is three times longer than
a. c is twice as long and
b. draw the roads. what fraction of the total length of the roads is the length of a? if road b is 7 miles longer than road a, what is the length of road c?

Answer 1

3 roads...a, b and c

b = 3a.....a = 1/3b
c = 2b.....b = 1/2c.....

a ------|
b ------|--------|------|
c ------|--------|------|------|------|------|

so a is 1/6 of the total road <===

if road b is 7 miles longer the a...
b = 3a....b = a + 7
a + 7 = 3a
7 = 3a - a
7 = 2a
7/2 = a
3.5 = a

b = 3a
b = 3(3.5)
b = 10.5

c = 2b
c = 2(10.5)
c = 21 <=====road C is 21

Answer 2

The fraction of the total length of the road is 1/10 the to the length of a and the value of c = 21 units.

Data;

• b = 3a
• c = 2b

Fraction of the total road is length of a

Let's try to find the total length of the road.

$b = 3a\\c = 2b\\b = c/2\\c/2 = 3a\\c = 6a$

Let's solve in terms of a

$a + 3a + 6a = 10a$

The length of the road in terms of a is 10a

The fraction of the total road is the length of a

$x = 10a\\a = \frac{1}{10}\\ x = length of the road$

1/10 is the fraction of a to the total length of the road.

b)

If b = 7 + a, c = ?

$b = 7 + a \\c = 2b\\c = 2(7+a)\\c = 14 + 2a$

but c = 6a

$6a = 14 + 2a\\4a= 14\\a = 14/4\\a = 7/2$

substitute the value of a

$c = 14 + 2a\\c = 14 + 2(7/2)\\c = 14 + 7\\c = 21 units$

From the calculations above, the fraction of the total length of the road is 1/10 the to the length of a and the value of c = 21 units.

Learn more on fractions here;

https://brainly.com/question/11562149