Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Question 17. A rabbit and a hedgehog had a race around a 550-meter-long circular track.  Both ran at constant speeds. The rabbit's speed was 10 meters a second, and the hedgehog's speed was 1 meter a second. They started at the same time. However,  the hedgehog ran in the opposite direction of the rabbit. When they met, the hedgehog immediately turned around and ran after the rabbit. How long after the rabbit  did the hedgehog reach the finish? To start this question, first we will have to find out  where the hedgehog and rabbit meet. To do this, we will do 10 meters a second plus 1 meter a  second. The speeds of the rabbit and hedgehog gives us 11 meters a second. We will take 550  meters, the length of the track, and divide it by 11 meters a second, giving us 50 seconds. At this point, we know that the speed of the hedgehog is equal to 50 meters.  Now, we divide by 10 meters a second the speed of the rabbit and get 5 seconds,  and we know that they met at the 50-second mark. So, how long after the rabbit did the hedgehog reach the finish? We do 50 seconds minus 5 seconds, and this gives us our answer,  which will be A, 45 seconds.

Video Summary

In a race around a 550-meter circular track, a rabbit and a hedgehog run at constant speeds of 10 m/s and 1 m/s, respectively, with the hedgehog running in the opposite direction. They meet after 50 seconds, calculated by dividing the track length by their combined speed of 11 m/s. Once they meet, the hedgehog turns to chase the rabbit. The rabbit finishes in 55 seconds (550 meters / 10 m/s), and the hedgehog reaches the finish 45 seconds after the rabbit. Thus, the hedgehog completes the race 45 seconds later than the rabbit.

Keywords

circular track

constant speeds

rabbit and hedgehog

race dynamics

meeting point