Solving for Time and Distance in Two Cars Traveling at Different Speeds

In summary, the conversation is about solving a problem involving two cars traveling at different speeds on a straight highway. The first question asks how much sooner the faster car will arrive at a destination 10 miles away, while the second question asks how far the faster car must travel to have a 15 minute lead on the slower car. The conversation includes a discussion on using the equation Distance = Speed x Time to solve the problem, as well as clarifications and corrections on the calculations.
  • #1
xyxaprilxyx
8
0
I'm very confused...


Please help me... It seems so simple..but its just not going into my head...

Two cars travel in the same direction along a straight highway, one at a constant speed of 55 mi/h and the other at 70 mi/h.

(a) Assuming that they start at the same point, how much sooner does the faster
car arrive at a destination 10 mi away?
(b) How far must the faster car travel before it has a 15 min lead on the slower
car?

How to solve a problem like this? Can Someone please Help?...



~April
 
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  • #2
Originally posted by xyxaprilxyx
How to solve a problem like this? Can Someone please Help?...
Start by using Distance = Speed x Time, and see what you can figure out.

For a) you know the distance, so find out how much time each takes.
 
  • #3
I got it.. but what about for the part ...
How far must the faster car travel before it has a 15 min lead on the slower
car?
How do get that? Do I just solve distance=speed x time then get the dispalcement between carSlower and carFaster?

So far this is what I got.
.18h for the time of car running 55mph and .14h for car running 70mph from that I subtracted and got .04 and that's the answer I got for part 1 of my question.

then
I solved for the distance for each car after 15 min.
and got
825mi for of car running 55mph and 1050mi for car running 70mph got the displacement and ended up with 225mi

Is that right?

There are no answers on the back of my book to check LOL
 
Last edited:
  • #4


Originally posted by xyxaprilxyx
Is that right?
No. For part b you found how far each went in 15 minutes. That's NOT what you were asked to find. You saw in part a that after 10 miles, the fast car is ahead by 0.04 Hrs, so how far does it have to travel to be ahead by 15 min? That's the question.

Let's review how to solve these problems.

Let 1 be the fast car, 2 be the slow car. So:
D = V1*T1
D = V2*T2

For part (a) we are given the distance and need to find the difference in time ΔT:
ΔT = T2 - T1 = D/V2 - D/V1

Which is what you did to solve a.

Now for part (b) you are given ΔT (15min =.25 Hr) and have to find D. So take the equation above and solve for D.
ΔT = D(1/V2 - 1/V1)

You can plug in the numbers and solve for D. Or you can realize that...Ah... all that stuff to the right of D is a constant. So, ΔT is just proportional to D. So... you do the rest.
 
  • #5
THANKS.. I came up with the answer -3.75mi..


Is that right?
 
  • #6
Originally posted by xyxaprilxyx
THANKS.. I came up with the answer -3.75mi..


Is that right?
Not even close. The distance is negative??
 

1. What is instantaneous velocity?

Instantaneous velocity is the velocity of an object at a specific moment in time. It is the rate at which an object's position changes at a given instant.

2. How is instantaneous velocity different from average velocity?

Instantaneous velocity is the velocity at a single point in time, while average velocity is the overall velocity of an object over a certain period of time. Instantaneous velocity takes into account any changes in velocity that occur during that specific moment, while average velocity does not.

3. How is instantaneous velocity calculated?

Instantaneous velocity is calculated by taking the derivative of an object's position function with respect to time. It can also be calculated by finding the slope of the tangent line to the position-time graph at a specific point.

4. What is the unit of measurement for instantaneous velocity?

The unit of measurement for instantaneous velocity is distance per time, usually represented as meters per second (m/s) in the SI system.

5. Why is instantaneous velocity important in physics?

Instantaneous velocity is important in physics because it allows us to analyze the motion of objects at a specific moment in time, rather than just looking at the overall motion. It also helps us understand the acceleration and changes in velocity of an object, which are key concepts in physics.

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