GK 2017 Q23
23. Eric and Eleanor are training on a 720 metre circular track. They run in opposite directions, each at a constant speed. Eric takes four minutes to complete the full circuit and Eleanor takes five minutes. How far does Eleanor run between consecutive meetings of the two runners?
- A 355 m
- B 350 m
- C 340 m
- D 330 m
- E 320 m
Grey Kangaroo 2017, Question 23. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 320 m
The ratio of the times taken to complete a circuit by Eric and Eleanor is 4:5. Therefore, since distance = speed × time and they both complete the same circuit, the ratio of their speeds is 5:4. Hence, since the total distance Eric and Eleanor cover between consecutive meetings is a complete circuit, Eleanor will run \(\tfrac{4}{4 + 5}\) of a circuit between each meeting. Therefore Eleanor will run \(\tfrac{4}{9}\) of 720 m which is 320 m between each meeting.
Solution © UK Mathematics Trust, from the GK 2017 solutions.