Question

Sebastian and his father went on a driving trip. They want to refuel the car and want to change tyres of the car in minimum time. Gas stations are located at an interval of $40\text{miles}$ and mechanic shops are located at an interval of $30\text{miles}$ from their house in same direction.

Find the minimum distance at which both the gas station and mechanic shop can be located at the same stop.

• A. $12\text{miles}$
• B. $120\text{miles}$
• C. $240\text{miles}$

Answer 1

The correct option is B $120\text{miles}$

As both the gas station and mechanic shop needs to be located at the same stop, the distance of the stop should be a multiple of both $40\text{miles}$ and $30\text{miles}$

For minimum distance, we need to find the LCM.

$40=2^3\times 5$
$30=2\times 3\times 5$

$\therefore$ LCM $=2^3\times 3\times 5=120$
(by excluding any repetitive prime factors from both the numbers)

Hence, the required distance is $120\text{miles}.$