Question

Calculate the constant of proportionality for distance-time pairs and arrange them in ascending order.

• A. (20 km, 4 hr) < (12 km, 2 hr) < (21 km, 3 hr) < (4 km, 0.5 hr)
• B. (12 km, 2 hr) < (20 km, 4 hr) < (21 km, 3 hr) < (4 km, 0.5 hr)
• C. (20 km, 4 hr) < (21 km, 3 hr) < (12 km, 2 hr) < (4 km, 0.5 hr)
• D. (20 km, 4 hr) < (12 km, 2 hr) < (4 km, 0.50 hr) < (21 km, 3 hr)

Answer 1

The correct option is A (20 km, 4 hr) < (12 km, 2 hr) < (21 km, 3 hr) < (4 km, 0.5 hr)

We know distance is directly proportional to time. As distance increases time taken to cover it also increases if speed is constant.
Ratio of distance and time is a speed which is constant of proportionality for this pair of quantities.

$Speed$ = $\frac{Distance}{Time}$

For pair 20 km, 4 hr
Speed = $\frac{20}{4}$ = 5 km/hr

For pair 12 km, 2 hr
Speed = $\frac{12}{2}$ = 6 km/hr

For pair 21 km, 3 hr
Speed = $\frac{21}{3}$ = 7 km/hr

For pair 4 km, 0.5 hr
Speed = $\frac{4}{0.5}$ = 8 km/hr

Arrangement of speeds(constant of proportionality) in ascending order of is: (20 km, 4 hr) < (12 km, 2 hr) < (21 km, 3 hr) < (4 km, 0.5 hr).