- #1
AN630078
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- Homework Statement
- Hello, I have been revising mechanics problems when I came across the question below. I do not know whether my approach would here be suitable and I typically struggle with these sorts of questions, not necessarily solving the simultaneous equations but formulating them to begin with. I have answered it fully but I would appreciate if anyone could comment upon whether my workings and methodology are applicable here. Also, the units given in the original question are miles, hours and mph, should I convert these to km or m and seconds or would this be unnecessary?
A car journey of 200 miles lasts 4 hours. It is partially spent on the motorway travelling at 70mph and the remainder on country roads travelling at 40mph.
Write this information as a pair of simultaneous equations and find the distances travelled on each road.
- Relevant Equations
- speed=distance/time
Equation 1:
Where t1=time spent on motorway
Where t2=time spent on country roads
t1+t2=4
Equation 2:
Using distance = speed * time
200 = 70*t1+40*t2
Rearrange equation 1 in terms of t1;
t1=4-t2
Substitute the rearranged form of equation 1 into equation 2:
200=70(4-t2)+40t2
200=280-70t2+40t2
200=280-30t2
Rearrange to find t2:
30t2=280-200
30t2=80
t2=80/30=8/3 hours (This is equation 3)
(Would units of hours be appropriate here?)
Substitute equation 3 into the original form of equation 1 to find t1:
t1+8/3=4
t1=4-8/3
t1=4/3 hours
Since I have now found t1 and t2 I can substitute this information to find the distance traveled on each of the roads;
distance=speed*time
distance on the motorway=70*4/3=280/3~93.3 miles to 3.s.f
distance on the country roads=70*8/3=320/3~106.7 miles to 3.s.f
Where t1=time spent on motorway
Where t2=time spent on country roads
t1+t2=4
Equation 2:
Using distance = speed * time
200 = 70*t1+40*t2
Rearrange equation 1 in terms of t1;
t1=4-t2
Substitute the rearranged form of equation 1 into equation 2:
200=70(4-t2)+40t2
200=280-70t2+40t2
200=280-30t2
Rearrange to find t2:
30t2=280-200
30t2=80
t2=80/30=8/3 hours (This is equation 3)
(Would units of hours be appropriate here?)
Substitute equation 3 into the original form of equation 1 to find t1:
t1+8/3=4
t1=4-8/3
t1=4/3 hours
Since I have now found t1 and t2 I can substitute this information to find the distance traveled on each of the roads;
distance=speed*time
distance on the motorway=70*4/3=280/3~93.3 miles to 3.s.f
distance on the country roads=70*8/3=320/3~106.7 miles to 3.s.f