Abdulla wrote:I'm confused with two things:
When the traveler travel towards each other why sometimes we equal the two equations together ad solve and the other time we add the two distance and = to the total distance.
i.e
R1= 240 T1= t+10 min. Total Dis=300
R2=160 T2 = t
Rephrasing my question : why we did 240 (t+1/6)+ 160t = 300 rather than
240(t+1/6)=160t and solve ..
When I have to use either way?
Towards each other
Lets say the distance between the travelers is
D
Traveler 1 , and his speed
V1
Traveler 2, and his speed
V2
time they will meet
T
So when they meet,
traveler 1, travels D1 = V1 * T
traveler 2, travels D2 = V2 * T
Also note that D1 + D2 = D
(V1 * T) + ( V2 * T ) = V T
Here V stands for their relative speed.
if you solve this equation for V:
V = V1+V2
so lets say the distance is 10 miles and V1=2miles/hr and V2=3miles/hr
so they will meet in : 10/(2+3) = 2 hrs
in 2 hrs,
Traveler 1 will travel 2x2 = 4 miles - D1
Traveler 1 will travel 2x3 = 6 miles - D2
Lets say they travel towards same direction
Traveller2...............3miles.......Traveler1......>
And they have 3 miles in between. Since V2>V1
Second guy will catch him at some point, after T hrs
When they travel the same distance, they will meet.
So Traveler 2 will travel
3 miles + X = V2 * T
Traveler 1 will travel
X = V1 * T
If you insert the latter equation into the former one:
3 miles + V1 * T = V2 * T
And if you solve for T:
T = 3 miles / ( V2-V1)
This is why we we subtract the velocities and divide the distance with this difference to find out when they will meet.
in our example:
T = 3/ (3-2) = 3 hrs
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