Molly left home and drove toward the ferry office at an average speed of 27 mph. Mark left two hours later and drove in the same direction but with an average speed of 45 mph. How long did Molly drive before Mark caught up?

I am terrible at word problems and this is a review question for a test. Can anyone help me? I have to solve it and write a statement.

To solve this problem, you'll want to come up with an algebraic equation that represents how far both Molly & Mark have travelled. Once the distance they have traveled is the same, Mark will have caught up with Molly. We want to find out how many hours Molly had to drive to reach that distance, and we know that the time Molly has been driving is 2 hours longer than the time Mark has been driving.

I'd use the following equation.
x = number of hours Mark has been driving
45x = 27(x+2)
This equation shows the distance Mark has traveled (driving 45 miles per hour for x hours) equal to the distance Molly has traveled (driving 27 miles per hour for x+2 hours). Solving for x will give you the number of hours Mark traveled, but remember to add the 2 hours to that, because we know that Mark left after Molly had already been driving for two hours.

in 2 hours, Molly was 54 miles ahead.

Mark was going 18 mi/hr faster, so it took him 54/18 = 3 hours to catch up.

But 3 is not the answer to the question ...

Molly: d1=V*t = 27 * 2 = 54 Miles head-

start.

d2 = d1 + 54.
45*T = 27*T + 54
18T = 54.
T = 54/18 = 3 h.

Molly's Time = 3 + 2 = 5 h.

Sure, I can help you with this word problem!

To solve this problem, we can use the formula: time = distance / speed.

Let's first find out how far Molly traveled before Mark caught up to her. Since she was driving for a certain amount of time before Mark started, we can calculate this using the formula: distance = speed * time.

We know that Molly's average speed was 27 mph. Let's assume she drove for t hours before Mark caught up.

So, the distance Molly covered before Mark caught up is 27 mph * t hours, which gives us a distance of 27t miles.

Now, let's focus on Mark. He was driving at an average speed of 45 mph. From the information given in the problem, we know that Mark left two hours after Molly. Since Mark catches up to Molly at some point, we can say that the time it took for Mark to catch up is the same as the time Molly drove before she was caught.

Using the formula for time, we can calculate how long Molly drove before Mark caught up: time = distance / speed. Substituting the values we know, we get t = (27t) / 45.

To solve this equation for t, we can cross-multiply: 45 * t = 27 * t. This simplifies to 45t = 27t.

Now, we can subtract 27t from both sides of the equation: 45t - 27t = 27t - 27t. This gives us 18t = 0, which means t = 0.

Therefore, Molly drove for 0 hours (or no time at all) before Mark caught up to her.

To write a statement, you can say: Molly did not have to drive any time before Mark caught up to her since he was faster and left two hours later.

I hope this explanation helps you understand how to solve this problem! Let me know if you have any further questions.