Travelator
When Andrew arrives at the end of the walkway, how far is he ahead of Bill?
Age
14 to 16
Challenge level
Problem
At the airport, there is a moving walkway $500\text m$ long, which moves at a speed of $4\text{km/h}$. Andrew and Bill step onto the walkway at the same time. Andrew walks with a steady speed of $6\text{km/h}$ on the walkway, whilst Bill stands still.
When Andrew arrives at the end of the walkway, how far is he ahead of Bill?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
Answer: 300 m
Finding the time on the walkway
Andrew: 6 km/h + 4 km/h = 10 km/h
500 m at 10 km/h = $\frac12$ km at 10 km/h takes $\frac1{20}$ of an hour.
Bill: 4 km/h
in $\frac1{20}$ of an hour, Bill travels 4000 m $\div$ 20 = 200 m
500 m $-$ 200 m = 300 m
Using proportion
Andrew: 6 km/h + 4 km/h = 10 km/h
Bill: 4 km/h
Distance and speed are proportional. Therefore, since Bill travels at $\frac{4}{10} = \frac{2}{5}$ of the speed of Andrew, he must travel $\frac{2}{5}$ of the distance. $\frac{2}{5}$ of 500 m is 200 m, so Bill is 300 m behind.