what is her speed?

Question

A freight train operator knows that on a 200 mile trip, if the freight cars aren't fully loaded, she can save 1 hour of travel time by increasing her normal speed by 10 miles per hour. What's her normal speed in miles per hour?

Answer 1

 

Hi Anna,

 

If we denote the normal speed as v

 

and the travel time with the speed of v as t,

 

we can express

 

     v·t = 200     (Eq. 1)

 

With the speed increased by 10 m/h,

 

the train can travel 200 miles in (t - 1) hours.

 

That is,

 

     (v + 10)·(t - 1) = 200

 

     v·t + 10t - v - 10 = 200

 

Plugging v·t = 200 into the equation right above,

 

we get

 

     10t - v = 10     (Eq. 2)

 

From Eq. 2, we get

 

     v = 10t - 10     (Eq. 3)

 

Plugging Eq. 3 into Eq. 1,

 

     (10t - 10)·t = 200

 

     10t² - 10t - 200 = 0

 

     t² - t - 20 = 0

 

     (t - 5)·(t + 4) = 0

 

     t = 5 or t = -4

 

As t represents travel time,

 

only t = 5 can be a meaningful solution.

 

Plugging t = 5 into Eq. 1,

 

     v·t = v·5 = 200

 

     v = 40

 

So, the normal speed v of the train is 40 miles per hour.

 

Hope this helps.