The time, \(T\) hours, taken for a bus to complete a fixed route is inversely proportional to its average speed, \(s\) km/h. At an average speed of \(40\) k...
Question 1 Report
The time, \(T\) hours, taken for a bus to complete a fixed route is inversely proportional to its average speed, \(s\) km/h. At an average speed of \(40\) km/h the route takes \(3\) hours.
- Find the value of the constant of proportionality. (1)
- Work out the time taken when the average speed is \(60\) km/h. (2)
Answer Details
Inverse proportion between two quantities means their product is always the same constant, \(k\), so \( T = \dfrac{k}{s} \), meaning time falls as speed rises.
(a) Substituting the known pair, \( s = 40 \) km/h giving \( T = 3 \) hours, the constant is \( k = T \times s = 3 \times 40 = 120 \) [1 mark].
(b) Using this constant with the new speed, \( T = \dfrac{120}{60} = 2 \) hours [2 marks].
Because \( T \) and \( s \) are inversely proportional, increasing the speed from 40 km/h to 60 km/h (a factor of \( 1.5 \)) reduces the time by the same factor, from 3 hours to \( 3 \div 1.5 = 2 \) hours, which is a useful check on the answer.
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