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Answer :
Final answer:
The first problem involving the two cars requires understanding relative speeds and distances while the succeeding questions involve understanding the positions and movements of clock hands in relation to time.
Explanation:
These problems involve applying principles of Mathematics, particularly in Physics and Geometry. For the first question, it involves relative speeds and distances to solve for the rate of car X. When the cars are moving in opposite directions, they meet after 2 minutes so the total distance they covered is twice the 1,320m track length. When they move in the same direction with car Y 220m behind when X reached the starting point, you can derive the speed difference. In the end, you can calculate the rate of car X. For the next questions, they involve concepts of angles in a clock, where every minute, the minute hand moves by 360 degrees/60 minutes = 6 degrees per minute and the hour hand by 360 degrees/12 hours = 0.5 degrees per minute. The differences in these speeds with the given conditions will allow you to solve the questions.
Learn more about Relative Speeds and Clock Angles here:
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Final answer:
The rate of car X is 46.2 km/h.
Explanation:
To calculate the rate of car X, we need to use the formula: rate = distance / time.
From the given information, we know that car X and car Y meet for the first time after 2 minutes when traveling in opposite directions. This means that car X has traveled half the distance of the circular track in 2 minutes.
Since the track is 1,320 m long, car X has traveled 660 m in 2 minutes.
Now, when car X and car Y travel in the same direction and start at the same point, car X reaches the starting point with car Y 220 m behind. This means that car X has traveled the entire distance of the circular track plus an additional 220 m in the same time it took car Y to travel the entire distance.
Let's calculate the time it took for car X to travel the entire distance of the circular track plus 220 m:
Distance = 1,320 m + 220 m = 1,540 m
Time = 2 minutes
Now, we can calculate the rate of car X:
Rate = Distance / Time = 1,540 m / 2 minutes = 770 m/minute
To convert the rate to kilometers per hour, we need to multiply it by 60 (since there are 60 minutes in an hour) and divide by 1,000 (since there are 1,000 meters in a kilometer):
Rate = 770 m/minute * 60 minutes/hour / 1,000 = 46.2 km/h
Learn more about calculating the rate of a car here:
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