2024 SJI P2 Q7

Jim and Ken embark on an expedition, travelling by foot on the same route separately. Jim travels 30 km on Day 1 and for each subsequent day, he travels 5% less than the previous day.

1. Find the total distance travelled by Jim up till Day 10.[3]

Ken starts his journey two days later, on Day 3, travelling 55 km on that day and for each subsequent day, he travels 2 km less than the previous day.

2. Show that the distance travelled by Ken on Day \(n\) is \((61-2n)\text{ km}\).[1]
3. Ken overtakes Jim on Day \(m\). Determine the value of \(m\).[4]

It is given that Ken would be able to complete the expedition on Day 17.

4. Determine the range of possible distances of the expedition.[3]
5. Explain why Jim may not complete the expedition eventually.[3]