Question 1196994: One speed skater starts across a frozen lake at an average speed of 7 m/s. Ten seconds later, a second speed skater starts from the same point and skates in the same direction at an average speed of 8 m/s. How many seconds after the second skater starts will the second skater overtake the first skater?
=______s
Answer by math_tutor2020(3817)   (Show Source):
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t = number of seconds that elapse after the 2nd skater starts
t+10 represents the number of seconds that the 1st skater has been moving since this skater got a 10 second head start.
In other words, the 1st skater has been moving for 10 seconds longer compared to the 2nd skater.
The 1st skater has a speed of 7 m/s
Using distance = rate*time, we know that the 1st skater travels a distance of 7(t+10) = 7t+70 meters
The 2nd skater has a speed of 8 m/s
distance = rate*time
distance = 8t
The 2nd skater meets up with the first skater when both skaters travel the same distance.
1st skater's distance = 2nd skater's distance
7t+70 = 8t
70 = 8t-7t
70 = t
t = 70
It takes 70 seconds for the two skaters to meet up.
After this point in time, the 2nd skater is going to pull ahead and stay ahead.
Answer: 70 seconds
Extra info:
70 seconds = 60 seconds + 10 seconds = 1 minute + 10 seconds
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