Rates, SM-Bank 023

Genghis and Kublai are shooting arrows at a target.

Genghis shoots an arrow every 3 seconds.

Kublai shoots an arrow every 8 seconds.

They shoot their first arrow together at 10:00 am.

How many more times will they shoot arrows at exactly the same time in the next 3 minutes? (2 marks)

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\(7\)

Show Worked Solution

\(\text{Lowest common multiple of 3 and 8}=24\)

\(\therefore\ \text{Every 24 seconds, the arrows are shot at the same time.}\)

\(\rightarrow\ \text{Arrows are shot at the same time:}\)

\(24, 48, 72, 96, 120, 144, 168\ \text{seconds}\)

\(\therefore\ 7\ \text{more times (time ≤ 180 seconds)}\)