Use .
So: Let and be the speed and time of the original train.
Then and . So . Substitute this into the equation to solve for .
Hi guys,
I need some help with a question that i just cant figure out how to solve. I have tried a lot but it does not seem to help. I am looking around and there is some complex math so i am guessing this might be a no brain-er for you guys.
Anyways the question is,
Two Trains travel a 105 km track each day. The express travels 10kmph faster and takes 30 minutes less than the normal train does. Find the speed of the express.
The answer is : 51.1 km/h ( the answer book tells me that)
I need to know how to solve to get to that answer. I cant find a way.
Thanks in advance, please get to me as soon as you guys can.
Thanks.
- Cluelessgeorge
Hey Turkeywilliams,
Thanks for the suggestion, I tried it out and it did not seem to generate the answer i needed.
Look below at my solution and see if anything else comes to your mind. Or anybody else, please consider looking and see if you can give me a solution.
SOLUTION :
d= vt
Let v and t represent speed and time.
(1) (v + 10)(t - 0.5) = 105
(2) vt = 105 ...v = 105/t
Sub Equation 2 into 1
(105/t + 10)(t - 0.5) = 105
105 - 55/t + 10t - 5 = 105
105t - 5 +10t^2 - 5t = 105t
10t^2 - 5t- 55 = 0
5 ( 2t^2 - t - 11) = 0
2t^2 - t - 11= 0
Using a graphing calculator...
t = -2.108 OR t = 2.608
As this is a real life situation, negative roots are eliminated as there is no negative time. Hence the only solution for time is 2.608.
Substitute t = 2.608 into Equation 1
(v + 10)(2.608 - 0.5) = 105
(v + 10)(2.108) = 105
v + 10 = 49.81
v = 39.81
This is my solution and according to my book it is wrong. Because my book says that the answer to this question should be 51.1 km/h.
So please reconsider your original thought process and see what you can figure out.
Thanks guys,
I really appreciate it.
- cluelessgeorge
You are trying to find or the speed of the express train. You solved for the speed of the original train. Also your is a bit off. Adding to your we get which is close to .
I get . Plug this into the equation and solve for . You should get .
Thank you very much
I did not consider that i was looking for V +10.
and I am a little surprised that you got different values for x than me.
I will trust you but i was wondering, why would that happen?
Thanks again for the help.
- cluelessgeorge