3.3 Two buses, bus A and bus B, both use the same bus stop. - Bus A runs every 10 minutes. - Bus B runs every 14 minutes. - Both buses are at the bus stop at 11 am. What time will both buses next be at the bus stop?

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1. We need to find the least common multiple (LCM) of the two intervals, $$10$$ minutes and $$14$$ minutes.

2. The prime factorization of $$10$$ is:
   $$
   10 = 2 \times 5
   $$

3. The prime factorization of $$14$$ is:
   $$
   14 = 2 \times 7
   $$

4. The LCM is obtained by taking the highest power of each prime number from both factorizations:
   $$
   \text{LCM} = 2 \times 5 \times 7 = 70 \text{ minutes}
   $$

5. Since both buses are at the bus stop at $$11:00$$ am, they will next be together in $$70$$ minutes.

6. To find the time, add $$70$$ minutes to $$11:00$$ am:
   $$
   11:00\, \text{am} + 70 \text{ minutes} = 12:10\, \text{pm}
   $$

Hence, both buses will next be at the bus stop at $$12:10\, \text{pm}$$.
Both buses will next be at the bus stop at 12:10 pm.

3.3 Two buses, bus A and bus B, both use the same bus stop. - Bus A runs every 10 minutes. - Bus B runs every 14 minutes. - Both buses are at the bus stop at 11 am. What time will both buses next be at the bus stop?

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