Two cyclists on a straight road
Two cyclists on a straight road
IP 1
7 marks
Towns \(P\) and \(Q\) are \(60\text{ km}\) apart on a straight road. Amy leaves \(P\) at 9.00 a.m. and cycles towards \(Q\) at a constant \(20\text{ km/h}\). Ben leaves \(Q\) at 9.30 a.m. and cycles towards \(P\) at a constant \(30\text{ km/h}\). Let \(t\) be the time in hours after 9.00 a.m.
- Write down Amy's distance from \(P\), and show that Ben's distance from \(P\) is \((75-30t)\text{ km}\) for \(t\ge\dfrac12\).[2]
- Find the time at which they meet and their distance from \(P\) at that moment.[3]
- Explain which cyclist completes the journey first.[2]
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(a) Amy \(20t\text{ km}\); Ben \(60-30\left(t-\dfrac12\right)=75-30t\) (b) 10.30 a.m., \(30\text{ km}\) from \(P\) (c) Ben, at 11.30 a.m. (Amy arrives at noon)
Need help? Join our IP Math tuition programme.
Learn more