2002 Paper 2 Q10

Year: 2002
Paper: 2
Question Number: 10

Course: LFM Pure and Mechanics
Section: Constant Acceleration

Difficulty: 1600.0 Banger: 1499.3

constant acceleration optimisation linear speed distance-time marathon minimum time quadratic equation maximum distance

Problem

A competitor in a Marathon of \(42 \frac38\) km runs the first \(t\) hours of the race at a constant speed of 13 km h\(^{-1}\) and the remainder at a constant speed of \(14 + 2t/T\) km h\(^{-1}\), where \(T\) hours is her time for the race. Show that the minimum possible value of \(T\) over all possible values of \(t\) is 3. The speed of another competitor decreases linearly with respect to time from 16~km~h\(^{-1}\) at the start of the race. If both of these competitors have a run time of 3 hours, find the maximum distance between them at any stage of the race.

No solution available for this problem.

Rating Information

Difficulty Rating: 1600.0

Difficulty Comparisons: 0

Banger Rating: 1499.3

Banger Comparisons: 4

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Problem source

A competitor in a Marathon of $42 \frac38$ km 
 runs the first $t$ hours of the race at a constant speed of 13 km h$^{-1}$
and the remainder at a constant speed of $14 + 2t/T$ km h$^{-1}$, where $T$ hours
is her time for the race. Show that the minimum possible value of $T$ over
all possible values of $t$ is 3.
The speed of another competitor decreases linearly with respect
to time from 16~km~h$^{-1}$ at the start of the race.  If both of these
competitors have a run time of 3 hours, find the maximum distance between
them at any stage of the race.

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