Inverse Variation Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
hardSpeed and travel time are inversely proportional for a fixed distance. At 60 km/h the trip takes 4 hours. How long at 80 km/h? Identify \(k\).
Solution
- 1 Fixed distance \(d = \text{speed} \times \text{time}\), so \(t = d/s\) — inverse variation.
- 2 \(k = d = 60 \times 4 = 240\) km.
- 3 Equation: \(t = 240/s\).
- 4 At \(s = 80\): \(t = 240/80 = 3\) hours.
Answer
3 hours; \(k = 240\) km
Distance (240 km) is the constant of variation. Higher speed → shorter time, confirming inverse variation.
About Inverse Variation
A relationship where : as one quantity doubles, the other halves—their product stays constant.
Learn more about Inverse Variation →More Inverse Variation Examples
Example 1 medium
(y) varies inversely with (x), and (y = 8) when (x = 3). Find (k) and the equation. Then find (y) wh
Example 3 mediumIf (y = k/x) and (y = 12) when (x = 5), find (y) when (x = 15).
Example 4 hardThe pressure (P) and volume (V) of a gas at constant temperature satisfy (PV = k). If (P = 4) atm wh