SOLUTION: Hi! I have another question on applications of linear equations. That is, word problems. A fast train was help up by a red-light signal for 16 minutes and made up for the lost t

Question 628316: Hi! I have another question on applications of linear equations. That is, word problems.
A fast train was help up by a red-light signal for 16 minutes and made up for the lost time on a 80-km stretch travelling at 10 kph faster than called by schedule. What is the scheduled speed of the train?
Thank you so much!
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A fast train was held up by a red-light signal for 16 minutes and made up
for the lost time on a 80-km stretch traveling at 10 kph faster than
called by schedule.
What is the scheduled speed of the train?
:
Change 16 min to hrs: 16/60 = hrs
:
Let s = the scheduled speed of the train
then
(s+10) = catch up speed of the train
:
Write a time equation time = dist/speed
:
Sched time - faster time = 16 min
- =
:
Multiply by 15s(s+10)
15s(s+10)* - 15s(s+10)* = 15s(s+10)*
:
Cancel the denominators, leaving
15(s+10)*80 - 15s(80) = 4s(s+10)
:
80(15s+150) - 1200s = 4s^2 + 40s
:
A quadratic equation
1200s + 12000 - 1200s = 4s^2 + 40s
0 = 4s^2 + 40s - 12000
:
simplify, divide by 4
s^2 + 10s - 3000 = 0
:
Factors to
(s+60)(s-50) = 0
s = 50 mph is the scheduled speed of the train
:
:
Check this, find the time of each trip
80/50 = 1.6 hrs
80/60 = 1.33 hrs
----------------
diff: .27 hr ~ 16 min

RELATED QUESTIONS
Hi I'm doing systems of linear equations & problem solving in math 103. Solving... (answered by KMST)

I'm working on this section in my Algebra book called Elimination by Addition... (answered by stanbon)

Could you please help me with some word problems my teacher has assigned? We were told... (answered by ankor@dixie-net.com)

hello, my name is arielena These problems are about algebra 1 : linear word problems. I... (answered by Maths68)

Hi, This is for a 7th math project on finding real life applications of algebra. I... (answered by richard1234)

Hi, How would I solve the following: Applications of Linear Equations Joe has a... (answered by scott8148)

hi i'm having an extreme amount of trouble setting up word problems for linear equations... (answered by Alan3354)

hi i'm having an extreme amount of trouble setting up word problems for linear equations... (answered by stanbon,fgwjr2003)

Hi. My teacher makes us use www.assistments.org and the problems on there are really hard (answered by stanbon)