Question

the amount of gasoline used by a car varies jointly as the distance travelled and the square root of the speed.Suppose a car used 25 liters on a 100 km trip at 100kph,about how many liters will it use on 1000 km trip at 64 kph?​

Answer 1

200 litres

Explanation:

let g be gasoline used, d the distance travelled and s the speed, then the equation relating the quantities is

g = kd
`√(s)` ← k is the constant of variation

To find k use g = 25, d = 100 and s = 100, then

25 = k × 100 ×
`√(100)` = k × 100 × 10 = 1000k ( divide both sides by 1000 )

0.025 = k

g = 0.025d
`√(s)` ← equation of variation

When d = 1000 and s = 64, then

g = 0.025 × 1000 ×
`√(64)` = 0.025 × 1000 × 8 = 200