FREE lectures this September + October | HSC Head Start + Exam Revision: book here | QCE Head Start: book here | VCE Exam Revision: book here

Welcome, Guest. Please login or register.

September 18, 2019, 12:52:13 pm

Author Topic: Confusing Motion Problem  (Read 194 times)  Share 

0 Members and 1 Guest are viewing this topic.

Srd2000

  • Trendsetter
  • **
  • Posts: 140
  • Respect: +15
Confusing Motion Problem
« on: January 31, 2019, 02:36:12 am »
0
Hi All, Iíve got a rather confusing problem on my hands. I believe Iím over complicating it with velocity-time graphs and simultaneous equations, but Iím not sure.

A person walks 50km in 4hrs. They start off walking 7km at a rate of x km/h. Then they ride a bike at 4x km/h for another 7km. Lastly, they drive a car the remaining distance at (6x+3) km/h. What is the value of x km/h?

Ans: x=3.5 km/h


My intial thinking was to do a velocity-time graph and use the area as mentioned, but that fell short when I introduced t1 and t2, respective times for when the person changes their transport. Then I tried solving it simultaneously, that got a negative answer. Iím sure that Iíve just overthought it or gone down a rabbit-hole.

Iíd much appreciate if someone could help out. Thank you!!!
2017 - Maths Methods (CAS), Chemistry, Physics

2018 - Specialist Maths, English, Japanese (SL)

lzxnl

  • Victorian
  • ATAR Notes Legend
  • *******
  • Posts: 3430
  • Respect: +207
Re: Confusing Motion Problem
« Reply #1 on: January 31, 2019, 03:42:13 pm »
+2
Hi All, Iíve got a rather confusing problem on my hands. I believe Iím over complicating it with velocity-time graphs and simultaneous equations, but Iím not sure.

A person walks 50km in 4hrs. They start off walking 7km at a rate of x km/h. Then they ride a bike at 4x km/h for another 7km. Lastly, they drive a car the remaining distance at (6x+3) km/h. What is the value of x km/h?

Ans: x=3.5 km/h


My intial thinking was to do a velocity-time graph and use the area as mentioned, but that fell short when I introduced t1 and t2, respective times for when the person changes their transport. Then I tried solving it simultaneously, that got a negative answer. Iím sure that Iíve just overthought it or gone down a rabbit-hole.

Iíd much appreciate if someone could help out. Thank you!!!

You know the total distance and total time. Use them.

First section: travels 7 km, 7/x hours
Second section: travels 7 km, 7/(4x) hours
Third section: 50 - 14 = 36 km, 36/(6x+3) hours
Add the times, set equal to 4 hours.
2012
Mathematical Methods (50) Chinese SL (45~52)

2013
English Language (50) Chemistry (50) Specialist Mathematics (49~54.9) Physics (49) UMEP Physics (96%) ATAR 99.95

2014-2016: University of Melbourne, Bachelor of Science, Diploma in Mathematical Sciences (Applied Maths)

2017-2018: Master of Science (Applied Mathematics)

2019-: ???

Accepting students for  VCE tutoring in Maths Methods, Specialist Maths and Physics! PM for more details

Srd2000

  • Trendsetter
  • **
  • Posts: 140
  • Respect: +15
Re: Confusing Motion Problem
« Reply #2 on: January 31, 2019, 05:31:37 pm »
0
Oooooh, that makes sense. I kept trying to use just the distance and speed to find x while ignoring time completely. My bad, oops.

Thank you, lzxnl!
2017 - Maths Methods (CAS), Chemistry, Physics

2018 - Specialist Maths, English, Japanese (SL)