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?

Question

UpStudy AI · Accepted Answer

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?

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Arithmetic Questions