I really need help with this one question on my math pretests and I have no idea what to do!

The question is:
Mandy begins bicycling west at 30 miles per hour at 11:00 am. If Liz leaves from the same point 20 minutes later bicycling west at 36 miles per hour, when will she catch Mandy?
Pretty please help me, all I need is really just some direction like what to do and if an answer is provided, how you got there. Thanks :)

Liz is going 6 mi/hr faster than Mandy.

By the time she starts, Mandy has gone (1/3)(30) = 10 miles

So, at 6 mi/hr, it will take 10/6 = 1 hr 40 min to catch up with Liz. So, that will be 2 hours after Mandy started, or 1:00 pm.

Or, you can plot both cyclists' positions as a function of t, the time (hours) spent traveling:
Mandy: 30t
Liz: 36(t - 1/3)

30t = 36(t - 1/3)
30t = 36t - 12
6t = 12
t = 2

Of course, I can help you with that question! To find when Liz will catch up with Mandy, we need to consider their speeds and the time difference between them.

Step 1: Convert the time difference into hours.
Liz leaves 20 minutes (1/3 of an hour) later than Mandy. This means we need to account for this time difference when comparing their distances.

Step 2: Determine the distance Mandy travels before Liz starts.
Since Mandy has a head start, we need to find the distance she covers before Liz begins. To do this, multiply Mandy's speed (30 mph) by the time difference (1/3 hour):
Distance = Speed * Time
Distance = 30 mph * 1/3 hour

Step 3: Write an equation for the distance traveled by both Mandy and Liz.
Let x be the time elapsed from when Liz starts. Mandy will have traveled x + 1/3 (the time difference) hours when Liz catches her. At that time, Liz will have traveled x hours. So we can write the equation:
Distance traveled by Mandy = Distance traveled by Liz
The distance traveled by Mandy can be calculated by multiplying her speed (30 mph) by the time elapsed (x + 1/3) hours. The distance traveled by Liz is her speed (36 mph) multiplied by the time elapsed (x) hours.

Step 4: Solve the equation to find x.
Plug in the values into the equation:
30 mph * (x + 1/3) = 36 mph * x
Simplify and solve for x:
30x + 10 = 36x
10 = 6x
x = 10/6
x = 5/3

Step 5: Convert x into minutes and find the time Liz will catch Mandy.
Since x is in hours, we need to convert it back to minutes.
1 hour is equivalent to 60 minutes, so 5/3 hours is:
(5/3) * 60 = 100 minutes

Liz will catch up with Mandy 100 minutes after she starts, or 1 hour and 40 minutes later.

Therefore, Liz will catch up with Mandy at 12:40 pm.

I hope this explanation helps you understand how to solve the problem!