Beth leaves her home on her bike, traveling down a long country road, at

the rate of 8 mph. Her brother, Brandon, left 15 minutes after Beth on his
golf cart along the same country road, traveling 12 mph. How long will it
take Brandon to catch up with Beth?

Beth has a 15 min head start at 8 mph , so 2 miles ahead

Brandon catches up at 4 mph (12 - 8)
... so it takes him 30 min to catch up

I don't get it. Do you right an equation?

Can someone help i don't understand

To find out how long it will take Brandon to catch up with Beth, we need to first determine the head start that Beth has.

Beth leaves her home 15 minutes earlier than Brandon, which can be converted to hours by dividing 15 minutes by 60: 15/60 = 0.25 hours.

Beth's head start is therefore 0.25 hours multiplied by her speed of 8 mph: 0.25 x 8 = 2 miles.

Now we can set up an equation to represent the distance covered by both Beth and Brandon until they meet.

Let t represent the time it takes for Brandon to catch up with Beth.

For Beth, the distance covered is given by d = 8t (since she travels at a rate of 8 mph).

For Brandon, the distance covered is given by d = 12(t - 0.25) (since he starts 0.25 hours later but travels at a faster rate of 12 mph).

Since they meet when they cover the same distance, we can set the two equations equal to each other:

8t = 12(t - 0.25)

Now we can solve for t:

8t = 12t - 3

3 = 12t - 8t

3 = 4t

t = 3/4

So it will take Brandon 3/4 hours to catch up with Beth.

Since 3/4 hours is equivalent to 45 minutes, it will take Brandon 45 minutes to catch up with Beth.