A Light was Seen at Intervals of 13 Seconds. It was Seen for the First Time at One Hour 54 Minute and 50 Seconds A.M and the Last Time at 3 Hours 17 Minutes and 49 Seconds A.M. How Many Times was the Light Seen?

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• Explanation

• Solution

Explanation

• A light was seen at intervals of 13 seconds.

• It was seen for the first time at one hour 54 minute and 50 seconds A.M.

• And the last time at 3 hours 17 minutes and 49 seconds A.M.

First, we will change “one hour 54 minute and 50 seconds” (1 x 3600 + 54 x 60 + 50 = 6890 seconds) and “3 hours 17 minutes and 49 seconds” (3 x 3600 + 17 x 60 + 49 = 11869) into seconds.

Now; we have a formula

a_n = a₁ + (n – 1)d ___________ (i)

a_n = 11869 seconds

a₁ = 6890 seconds

d = 13 seconds (given)

By putting the value in this equation; we can easily find out the value of n.

To Find

How many times was the light seen = ?

Solution

1 h 54 min 50 sec = 1 x 3600 + 54 x 60 + 50 = 6890 seconds

3 h 17 min 49 sec = 3 x 3600 + 17 x 60 + 49 = 11869 seconds

Now;

a_n = a₁ + (n – 1)d

a_n = 11869 seconds

a₁ = 6890 seconds

d = 13 seconds (given)

By putting the values;

11869 = 6890 + (n – 1)13

11869 – 6890 = (n – 1)13

4979 = (n – 1)13

4979/13 = n – 1

383 = n – 1

383 + 1 = n

384 = n

How many times was the light seen = 384 answer

Conclusion

A light was seen at intervals of 13 seconds. It was seen for the first time at one hour 54 minute and 50 seconds A.M and the last time at 3 hours 17 minutes and 49 seconds A.M and 384 times the light was seen in total.