2026 NYGH P1 Q2

After charging for an hour, Tom’s e-bike can travel a distance of \(x\) kilometres whereas Jen’s e-bike can travel a distance of \((x-1)\) kilometres.

1. Write down an expression, in terms of \(x\), for the total charging time in hours, needed for Tom’s e-bike to travel a distance of \(48\) kilometres.[1]
2. The difference in charging time for both e-bikes to travel a distance of \(48\) kilometres is \(0.5\) hours. Write down an equation in \(x\) to represent this information and show that it reduces to \(x^2-x-96=0\).[2]
3. Solve the equation \(x^2-x-96=0\), giving your answers to 2 decimal places.[2]
4. Hence, find the charging time needed for Jen’s e-bike to travel a distance of \(48\) kilometres.[1]