Question

the cost,$c, of transporting goods is directly proportional to the distance covered ,d km.
the cost of transporting goods over a distance of 60 km is $100.
(1) find an equation connecting c and d.
(2) find the cost of transporting goods over a distance of 45 km.
(3) if the cost of transporting goods is$120, calculate the distance covered.
(4) draw the graph of c against d
​

Answer 1

✪ᴀɴsᴡᴇʀ✪

Equation

Here,

$\to c \propto d$

$\to c = kd... (1)$

60 Km of good transport cost $100,so

$\to \ 100= k\times 60Km$

$\to k = \ \frac{100}{60}/Km$

$\to k = \ \frac{5}{3}/Km$

Substituting in (1),we get

$\to\boxed{c = \frac{5}{3}d} ... (2)$

This is the required equation.

Cost for transporting over 45Km

Here,

Distance, $d = 45\:Km$

Using equation (2),

$\to c = \ \frac{5}{3}\times 45$

$\to c = \ 5\times 15$

$\to c = \ 75$

Thus, cost of transporting over 45 Km is $75.

Distance for cost of $120

Here,

Cost, $c = \ 120$

Using equation (2),

$\to 120 = \frac{5}{3}d$

$\to d = 120 \times \frac{3}{5}$

$\to d = 24 \times 3$

$\to d = 72\:Km$

Thus, $120 will cover 72 Km

Graph

Graph between 'c' and 'd' is a straight line in the first quadrant which pass through the origin (0,0).

[With this hint, you can draw the graph :)]