Calculate Initial Speed Driving on a Crowded Freeway

[Robb380]

Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 4.5 mi/h, the time to go one mile decreases by 9 s. What was your original speed?

I've been working on this for 2 hours, I can't seem to get the formula right.

 

[tiny-tim]

Welcome to PF!

Hi Robb380! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[Robb380]

I've decided that the v=d/t is not the way to go and that (vi) initial velocity is vi- 4.5mph=vf or final velocity (vf) = vi + 4.5 mph. and the time is t-9. going 1 mile gives me
initial distance= 0
final distance= 1
initial velocity(vi)= vf-4.5 mph
final velocity(vf)= vi+4.5
time for (vi) mph= t
time for (vf) mph=t-9
What i can't seem to do is find an equation that can help me find the initial velocity. I've tried different ones but they don't see to fit well, I am thinking i can solve for t and from there find (vi) but I am not sure how

 

[SteamKing]

First of all, I suggest you convert your speeds to common units. You have speed in miles per hour and time in seconds. A better approach would be to convert the change in speed, 4.5 mph, to the equivalent speed in feet per second.

You know that at your original speed, it took ti seconds to travel 1 mile, or 5280 feet. After increasing speed by 4.5 mph, it took 9 fewer seconds to travel 1 mile. Think you can work out the original speed now?

 

[Robb380]

Not really because I don't have a formula to use to solve for anything, i tried a binomial equation but that came out wrong, I retraced to see if I wasn't converting the units but I was, I tried putting everything into miles per second but I keep getting stuck when trying to solve for t so that I can solve for (vi). What I need is to figure out is how to get either (ti), (vi), or i might need both

 

[SteamKing]

It's a simple problem to set up. The only formula you need is v = d / t and a little algebra.

 

[tiny-tim]

Hi Robb380!

Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next.

So the initial speed is obviously 1/t mph, isn't it?

Carry on from there …

what do you get? ​

 

[HallsofIvy]

Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next.

Hi Robb380!


So the initial speed is obviously t mph, isn't it?

Assuming that t is measured in hours.