Question

Use least commin multiple or greatest common divisor to solve the prob

Factors and multiples
ANSWERED
asked 2021-08-09
Use least commin multiple or greatest common divisor to solve the problem.
Rob can complete his bus route in 6 hours. Joan can complete her bus route in 4 hours. If they both left the terminal at 3:00 am and after each completed route returned to the terminal, determine the next time they would leave the terminal at the same time.
A) 9:00 am
B) 7:00 am
C) 3:00 pm
D) Not enough information given to tell.

Answers (1)

2021-08-10
Step 1
Given- Rob can complete his bus route in 6 hours. Joan can complete her route in 4 hours. If they both leave the terminal at 3:00 am and after each completed route return to the terminal,
To find- The next time they would leave the terminal at the same time.
Concept Used- To find the time at which they leave terminal , the concept of least common multiple can be used here.
Step 2
Explanation- As per the question, Rob can complete his bus route in 6 hours. Joan can complete her route in 4 hours.
Here using the least common multiple, so we have to find the multiples of 4 and 6 which are given below,
Multiple of \(\displaystyle{4}={4},{8},{12},{16},{20}\ldots\ldots\)
Multiple of \(\displaystyle{6}={6},{12},{18},{24},{30}\ldots\ldots.\)
From the above multiples, we see that 12 is the common multiple of 4 and 6.
So, the least common multiple of 4 and 6 is 12.
So, they will meet at the terminal after \(\displaystyle{\left({3}:{00}{a}{m}+{12}{h}{o}{u}{r}{s}\right)}={3}:{00}\) pm.
Answer: Hence, the next time they would leave the terminal at 3:00 pm, which is option C.
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