A delivery company uses the formula \(s=\dfrac{d}{t}-c\) to estimate a driver's average speed, \(s\) mph, on a delivery round, where \(d\) is the distance t...
Question 1 Report
A delivery company uses the formula \(s=\dfrac{d}{t}-c\) to estimate a driver's average speed, \(s\) mph, on a delivery round, where \(d\) is the distance travelled in miles, \(t\) is the time taken in hours, and \(c\) is a fixed correction constant for traffic delays.
- Make \(t\) the subject of the formula. (3)
- Use your formula to work out \(t\) when \(s=40\), \(d=90\) and \(c=5\). (2)
Answer Details
The formula \(s=\dfrac{d}{t}-c\) links speed, distance, time and a correction constant; rearranging it to make \(t\) the subject means isolating the fraction \(\dfrac{d}{t}\) first, then inverting.
(a) Adding \(c\) to both sides isolates the fraction: \(s+c=\dfrac{d}{t}\). Multiplying both sides by \(t\) and then dividing by \((s+c)\) gives \(t=\dfrac{d}{s+c}\). [3 marks]
(b) Substituting \(d=90\), \(s=40\) and \(c=5\): \(t=\dfrac{90}{40+5}=\dfrac{90}{45}=2\) hours. [2 marks]
The correction constant \(c\) must be added to \(s\) before dividing into \(d\), not added afterwards: \(t=\dfrac{d}{s}+c\) would be a different (incorrect) formula, since \(c\) is grouped with \(s\) on the same side of the original equation.
Download The App On Google Playstore
Everything you need to excel in your exams
