Question

5 bells toll together at 9:00 am and toll at intervals of 2, 4, 6, 8, and 10 seconds respectively. Find by 9:40 am, how many times do they toll together?

(a) 20 times
(b) 19 times
(c) 30 times
(d) 21 times

Answer 1

To determine the number of times the bells toll together by 9:40 am, the least common multiple (LCM) of the tolling intervals is calculated, which is every 2 minutes. Dividing the 40-minute span by the 2-minute interval yields 20 tolls, plus one initial toll at 9:00 am, resulting in a total of 21 times.

Step-by-step explanation:

The question involves finding out the number of times 5 bells toll together between 9:00 am and 9:40 am, given their individual tolling intervals. Since the intervals are 2, 4, 6, 8, and 10 seconds, we first need to find the least common multiple (LCM) of these numbers to determine when the bells will toll together. The LCM of 2, 4, 6, 8, and 10 is 120 seconds, or 2 minutes.

The bells will toll together every 2 minutes starting at 9:00 am. The time period from 9:00 am to 9:40 am is 40 minutes. So, to find the number of times the bells toll together, we divide 40 minutes by 2 minutes per toll, which gives us 20 tolls. However, we must add one more toll for the initial tolling at 9:00 am.

Therefore, the bells toll together 21 times by 9:40 am. The correct answer is (d) 21 times.

Answer 2

The bells will toll together 20 times between 9:00 am and 9:40 am.

The correct answer is (a) 20 times.

To find out how many times the bells toll together between 9:00 am and 9:40 am, we need to find the least common multiple (LCM) of the given time intervals (2, 4, 6, 8, and 10 seconds).

The time intervals are: 2, 4, 6, 8, 10.

The prime factorization of each number is as follows

2=2^1

4=2^2

6=2^1 ×3^1

8=2^3

10=2^1 ×5^1

To find the LCM, we take the highest powers of all prime factors involved:

LCM=2 ^3 ×3 ^1 ×5^1 =8×3×5=120

So, the bells will toll together every 120 seconds.

Now, let's find out how many 120-second intervals there are between 9:00 am and 9:40 am:

40 minutes/ 1 minute÷60 seconds =2400 seconds

2400 seconds/ 120 seconds per interval =20

Therefore, the bells will toll together 20 times between 9:00 am and 9:40 am.

The correct answer is (a) 20 times.