# Help with visualizing this problem

Help with visualizing this problem....

I am having a bit of brain lock-up at the moment...and just can not seem to see my way through this problem.

A vehicle takes "t" to travel one mile. If the vehicle's speed was 5 mph faster then the "t" to travel the one mile would of been 11 seconds less. What is the original speed of the vehicle.

I first thought of the formula d=vt but even with looking at the problem with v1 and v2 and/or t1 and t2 with even making a bunch of drawings ...I am just at a loss. I am beginning to think I do not have enough information.

Can someone give me a gentle nudge in the right direction to get me back on track?

Thanks

Tide
Homework Helper
You have enough information. You can write two equations with two unknowns, v and t. The rest is just algebra.

You just need to get your variables straight.

Let's try splitting the two cases up into vehicle 1 and vehicle 2 and define the following variables:

Vehicle 1:
distance: d_1
velocity: v_1
time: t_1

Vehicle 2:
distance: d_2
velocity: v_2
time: t_2

Ok. So far we've used no information. Let's take each phrase and try to extract information. Again, I'm going to treat the two cases as two different vehicles.

"A [the first] vehicle takes "t" to travel one mile."

t_1 = t
d_1 = 1

"If the [second] vehicle's speed was 5mph faster...

v_2 = v_1 + 5

"... then the 't' to travel one mile..."

d_2 = 1 = d_1

"...would of been 11 seconds less."

t_2 = t_1 - 11 = t - 11

So now, what you thought was to look at the relationship, d=vt. Let's see what we get when we write out this equation for each vehicle (making substitutions based on our above equations).

Vehicle 1:
d_1 = v_1 * t_1
1 = v_1 * t

Vehicle 2:
d_2 = v_2 * t_2
1 = (v_1 + 5) * (t - 11)

So you have two equations and two unknowns:
1 = v_1 * t
1 = (v_1 + 5) * (t - 11)

Thanks! Woke up this morning realizing that I was over thinking this problem. Casey