Question

A northbound bus and a southbound bus are at a bus stop at the same time. The northbound bus returns to the bus stop every 20 minutes and the southbound bus returns to the bus stop every 25 minutes. How long will it be before both buses are the bus stop at the same time again?
A. 50 minutes
B. 100 minutes
C. 200 minutes
D. 500 minutes

If you could explain how you got the answer that'll be great!

Answer 1

The question is essentially asking for the least common multiple of 20 and 25. There are several ways you can find the LCM. One easy way is to divide the product by the GCD (greatest common divisor).

GCD(20, 25) = 5 . . . . . see below for a way to find this, if you don't already know

LCM(20, 25) = 20×25/GCD(20, 25)

... = 500/5 = 100

The buses will be there together again after ...

... B. 100 minutes

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You can also look at the factors of the numbers:

... 20 = 2²×5

... 25 = 5²

The least common multiple must have factors that include all of these*, so must be ...

... 2²×5² = 100

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* you can describe the LCM as the product of the unique factors to their highest powers. 20 has 2 raised to the 2nd power. 25 has 5 raised to the 2nd power, which is a higher power of 5 than is present in the factorization of 20. Hence the LCM must have 2² and 5² as factors.

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You can also look at the factorization of 20 and 25 to see that 5 is the only factor they have in common. That is the GCD, sometimes called the GCF (greatest common factor).

Answer 2

Every 100 minutes. You would need to find the lcm. So 20x5=100 and 25x4=100