
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
January 11th, 2017, 08:54 PM  #1 
Member Joined: May 2015 From: Australia Posts: 59 Thanks: 6  Year 10 Motion problem
Question: A motor cyclist makes a trip of 500km. If he had increased his speed by 10km/h, he could have covered 600km in the same time. What was his original speed? Answer: 50km/h I tried solving it by using d=st st + t(s+10) = 500 + 600 st + st + 10t = 1100 2st + 10t = 1100 I think I'm doing it wrong though. Could someone help me? Last edited by skipjack; January 12th, 2017 at 04:29 AM. 
January 11th, 2017, 10:06 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,460 Thanks: 489 Math Focus: Yet to find out. 
The key here is that in both cases, the time is the same. So for the first case, we have the following, $\displaystyle 500 = \frac{1}{2}v t$ And so, $\displaystyle t = \frac{1000}{v}$. Now if we follow a similar procedure, this time having a known value for t, we have, $\displaystyle 600 = \frac{1}{2} (v + 10) * \frac{1000}{v}$ $\displaystyle 1200 = \frac{1000 \cancel{v}}{\cancel{v}} + \frac{10000}{v}$ $\displaystyle (1200  1000)v = 10000$ $\displaystyle \therefore v = 50km/h.$ Note that I have been sloppy with labeling my units here. Always remember what units you are working with! Last edited by skipjack; January 12th, 2017 at 03:51 AM. 
January 12th, 2017, 04:27 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 18,247 Thanks: 1439  As distance increase = (speed increase) * time, time = 100km/(10km/h) = 10h, and so the original speed = 500km/(10h) = 50km/h. If you prefer to use your variables, you can write that as shown below. Subtracting st = 500km from (s + 10km/h)t = 600km gives (10km/h)t = 100km, and so t = 10h. Hence s = 500km/t = 50km/h. 
January 12th, 2017, 05:51 AM  #4 
Member Joined: May 2015 From: Australia Posts: 59 Thanks: 6 
I understand your solution, but in my textbook there is an example preceding the question. In the example, it adds the variables instead of subtracting it. Is there a way to do it similar to the example method or not?

January 12th, 2017, 07:10 AM  #5 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,081 Thanks: 698 Math Focus: Physics, mathematical modelling, numerical and computational solutions  That's a different problem entirely, so it has a different solution. Don't compare them in terms of "adding things" or "subtracting things" because you shouldn't work like that. If you stick to the formulas, you'll be fine.


Tags 
motion, problem, year 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Algebra  Year 10 Problem Solving  pianist  Algebra  2  January 10th, 2017 02:44 AM 
Year 7 Math Problem (Puzzle)  lydback  New Users  1  August 10th, 2016 01:03 AM 
Physics: Projectile Motion/Relative Motion  edwinandrew  Physics  0  February 26th, 2014 04:30 PM 
A problem for the year 2012  icemanfan  Math Events  0  March 6th, 2012 07:21 PM 
Year 8 maths problem...URGENT!  claudeluvstwilight  Elementary Math  3  June 30th, 2008 05:03 AM 