Question

A and B are jogging around a park's circular track which has a perimeter of 1.2 km. They start from the same point at 6:00 a.m. and run in opposite directions. A's speed is 5 km/h, and B's speed is 7 km/h. At what time will they meet for the fifth time?

• A. 6:25 AM
• B. 6:30 AM
• C. 6:45 AM
• D. 7:00 AM

Answer 1

Answer:

B. 6:30 AM

Track perimeter (= 1.2) km

Since they run in opposite directions, relative speed:

$5 + 7 = 12 \text{ km/h}$

Time for one meeting:

$\frac{1.2}{12} = 0.1 \text{ hour}$

$0.1 \text{ hour} = 6 \text{ minutes}$

So they meet every 6 minutes.

For the 5th meeting:

$5 \times 6 = 30 \text{ minutes}$

Starting time = 6:00 a.m.

$6:00 + 30 \text{ minutes} = 6:30 \text{ a.m.}$

So, they will meet for the fifth time at:

$\boxed{6:30\ \text{a.m.}}$