Question

The following table shows the rate of change of distance with time, which remains constant. Find the values of
A and B in the given table.

Distance traveled (mi)	50	A	150
Time taken (h)	2	3	B

• A. A = 5, B = 60
• B. A = 50, B = 3
• C. A = 75, B = 6
• D. A = 45, B = 6

Answer 1

The correct option is C A = 75, B = 6

The table shows the rate of change of distance with time.

The first rate can be written as $\frac{50}{2}.$

By simplifying the fraction, we can write the the rate of change as $\frac{25}{1}.$

Since the given ratios are equivalent, they should be equal to $25:1.$
$\frac{\text{Distance traveled (mi)}}{\text{Time taken (h)}}=\frac{A}{3}=\frac{25}{1}$
$=\frac{A}{3}=\frac{25\times 3}{1\times 3}=\frac{75}{3}$

So, the distance covered in $3h$ will be $75mi.$

To find $B$, we will use the same equivalent ratio.
$\frac{\text{Distance traveled (mi)}}{\text{Time taken (h)}}=\frac{150}{B}=\frac{25}{1}$
$\frac{150}{B}=\frac{25\times 6}{1\times 6}=\frac{150}{6}$

Time taken to cover $\text{150 mi is 6 h.}$

Hence, $\text{A = 75 and B = 6}.$