Waiting for a Friend: Solving a Time Difference Problem

[black_hole]

Homework Statement

You and a friend each drive 50 km. You travel at a uniform speed of 91.4 km/hr and your friend travels at a constant speed of 88.3 km/hr. How long will you wait for your friend?

Homework Equations

The Attempt at a Solution

So I thought I could just set up a ratio and cross-multiply to get the hrs. traveled by each person. I got .547hrs. for "me" and .566hrs. for "my friend". Then subtract, the difference being the answer. However, I am doing this on a computer-generated exercise and it is telling me that .019hrs. is incorrect. Why isn't this right?

 

[Redbelly98]

It looks like you did this correctly, I get the same answer. It could be they expect a different number of significant figures in the answer, or they expect different time units for some reason.

 

[tomcue]

I would approach this problem by first converting the speeds from km/hr to m/s to make the units consistent. Then, I would use the formula d = vt to calculate the time it takes for each person to travel 50 km. For you, it would be t = 50 km / (91.4 km/hr * 1000 m/km * 1 hr/3600 s) = 0.0154 hrs. For your friend, it would be t = 50 km / (88.3 km/hr * 1000 m/km * 1 hr/3600 s) = 0.0160 hrs. The difference between these two times is 0.0006 hrs, which is equivalent to 2.16 seconds. Therefore, you would only need to wait for approximately 2 seconds for your friend to catch up to you.

The reason why your previous approach did not give the correct answer is because you were using the average speed of each person instead of their actual speeds at any given time. By using the formula d = vt, we are able to account for the changing speeds and accurately calculate the time it takes for each person to travel the given distance.