A woman works at a law firm in city A which is about 65 miles from city B. She must go to the law library in city B to get a document. Find how long it takes her to drive round-trip if she averages 50 mph .

Question

triciaal · Answer

distance d = velocity, v * time, t
d = vt  how would you find t?
distance is round trip  65 miles times 2 = 130 miles
velocity is the average speed = 50 mph
find the time by putting in the known values in the equation  and solving for t

triciaal · Answer

another way to look at is 
50 times 1mile travelled in one hour 
divide by 50 means 1 mile travelled in 1/50 hour
65 miles = 65*1mile so it would take 65*1/50 hour
this is one way so the round-trip would take twice the time for 1-way = 2*65*1/50 and the time is in hours

triciaal · Answer

any questions?

mathstudent55 · Answer

Since the problem mentions an average speed, it's a good idea to start with an equation for the average speed.

$average~speed = \dfrac{distance}{time}$

We can use the variables s = average speed, d = distance, and t = time to make it simpler:

$s = \dfrac{d}{t}$

The problem is asking for the time, so we solve out equation for t, time:

Multiply both sides by t:

$st = d$

Divide both sides by s:

$t = \dfrac{d}{s} $

Now we know that the time is the distance divided by the average speed.

We need a distance and an average speed to find the time. The cities are 65 miles apart, so a round trip is $2 \times 65 ~miles = 130 ~miles$. That's our distance. The average speed is given as 50 mph.

$t = \dfrac{d}{s} $

$\large t = \dfrac{130~miles}{50 \frac{miles}{hour} } $

$t = 2.6 ~miles \times \dfrac{hour}{miles} $

$ t = 2.6 ~hours$

As you can see, the units cancel out to give us hours, which is a correct unit for time.

anonymous · Answer

Thank you, to the both of you guys. I appreciate it.

triciaal · Answer

You are welcome