Maths

Question

2 cars race around a circular track, in opposite directions, at constant speeds. They start at the same point and meet every 30.0 seconds. If they move in the
same direction, they meet every 120.0 seconds. If the track is 1800 meters long, what is the speed of first car?

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Nikhilaery · Answer

Case (1) when in the same direction

Let's say "y" is stationery, therefore, in that case we can say the first car is traveling towards the second car at (x+y)

This gives us the first equation 
I.e. (x+y) * 30 = 1800

Which gives me, x + y = 60 m/s

Case (2) when both are moving in th same direction

Again, assuming that the second car is stationery and the first car's speed is greater than the second car's (one of the cars has to be faster than the other for them to meet each other when moving in the same direction).

Thus gives us our second equation
(x-y)*120 = 1800 
(x-y) = 15 m/s

Solving equations (1) and (2) - Adding them.

2x = 75
x = 37.5 m/s

solving for second car's speed 'y'
x-y = 15 
y = x - 15 
y = 37.5 - 15 = 22.5 m/s

Assuming that the first car is the fastest of the two, we have x = 37.5 m/s

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sashiim20 · Answer

Hi.. there is small calculation mistake...

Should be  = \frac{1800}{120} = 15  m/s

Nikhilaery · Answer

Hi.. there is small calculation mistake... Should be = \frac{1800}{120} = 15 m/s Thanks, sashiim20 . I calculated that just before sleeping, perhaps the reason why an error occurred

sashiim20 · Answer

Speed = Distance / Time

Distance  = 1800  m

Lets speed of cars be  x  and  y

When cars race in opposite direction, relative speed will be added  = x + y

Time when cars race in opposite direction  = 30  s

When cars race in same direction, relative speed will be subtracted  = x - y

Time when cars race in same direction  = 120  s

x + y = \frac{1800}{30} = 60  m/s

x - y = \frac{1800}{120} = 15  m/s

x + y = 60  ------- ( i )

x - y = 15  -------- ( ii )

Adding equations ( i ) and ( ii ) we get;

2x = 75

x = 37.5  m/s

Substituting value of  x  in ( i ), we get;

y = 60 - 37.5 = 22.5  m/s

If first car is the fastest of the two cars, speed of  x= 37.5  m/s

sashiim20 · Answer

Thanks, sashiim20 . I calculated that just before sleeping, perhaps the reason why an error occurred

:thumbup:

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