The distance $s$ (in km) travelled by a car varies directly as the square of its speed $v$ (km/h) and inversely as its fuel consumption rate $f$ (L/h). When the car travels at $v=60$ km/h with a fuel consumption of $f=5$ L/h it covers $s=180$ km.

(a) Find the constant of variation $k$.
(b) Using this constant, determine the distance the car will travel if its speed is increased to $80$ km/h and its fuel consumption rises to $8$ L/h.
(c) By what percentage does this new distance exceed the original 180 km? Give your answer to the nearest whole percent.

Question

The distance $s$ (in km) travelled by a car varies directly as the square of its speed $v$ (km/h) and inversely as its fuel consumption rate $f$ (L/h). When the car travels at $v=60$ km/h with a fuel consumption of $f=5$ L/h it covers $s=180$ km.

(a) Find the constant of variation $k$.
(b) Using this constant, determine the distance the car will travel if its speed is increased to $80$ km/h and its fuel consumption rises to $8$ L/h.
(c) By what percentage does this new distance exceed the original 180 km? Give your answer to the nearest whole percent.

Accepted Answer

k = 0.25; distance = 200 km; percentage increase ≈ 11%

Neco Model Questions Vol1 2018 Mathematics Question 13

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