Car and time

[Viper83]

how much time did it take a certain car to travel 400 km?

1. the car traveled the first 200 km in 2.5 hrs
2. if the car's average speed had been 20 km/hr greater than it was, it would have traveled the 400 km in 1 hr less than it did.

From the prompt we get 400=rt

Is this setup correct?
1. is obviously insufficient because we dont know anything about the additional 200 km.
2. we have 400=rt from the prompt. From statement 2 we get 400=(r+20)(t-1). Now we have 2 equations and can solve for t. Is this correct? Answer is B

[amit2k9]

in b

400/(s) - 400/(s+20) = 1
so you get s(s+20) = 8000
where s can be = 20 or so. Hence sufficient.

in your case
st = (s+20)(t-1) = st-s+20t-20
so, s+20 = 20t

as st=400 hence t=400/s
so substituting for s will give t too.
sufficient.

[Anurag@Gurome]

Is this setup correct?
1. is obviously insufficient because we dont know anything about the additional 200 km.
2. we have 400=rt from the prompt. From statement 2 we get 400=(r+20)(t-1). Now we have 2 equations and can solve for t. Is this correct?

Yes, it's correct but careless.
There is more to solving the equations than just saying "we have two equations in two unknown, hence we can solve..". That statement only holds strong when the equations are linear and independent of each other.

In this case, rt = 400 ........ (1)
And, (r + 20)(t - 1) = 400 .... (2)

Now replacing 400 in (2) by rt from (1), we have

• --> (r + 20)(t - 1) = rt
  --> (rt + 20t - r - 20) = rt
  --> (20t - r - 20) = 0 ......... (3)

Now, replacing r = 400/t from (1) in (3),

• --> (20t - 400/r - 20) = 0
  --> (20t² - 20t - 400) = 0
  --> (t² - t - 20) = 0 .......... (4)

Solving (4) we get, t = 5 or t = -4

Now in this case t = -4 is not possible, hence t = 5.
BUT what if the equation gave two possible solution for t? In that case statement 2 wouldn't had been sufficient.

[Viper83]

Thanks Anurag, so in this kind of question one should actually solve to get the answer since it is a quadratic equation?

[Anurag@Gurome]

Thanks Anurag, so in this kind of question one should actually solve to get the answer since it is a quadratic equation?

In my opinion, yes.

[anuragvaid]

Anurag_Gurome,

Thanks for the fundoo explanation and the absolutely correct way to approach these quesns...

Just a quickie - I think the correct value of T will be 5 not 4. Thats cos, T = 5 or T=-4 will be the roots here.....

Anurag

[anuragvaid]

Anurag,

Its my mistake.....U had indeed correctly mentioned the solution to be 5...dunno, Y I read 4....

Nevertheless, my two cents !!!

Anurag

[Anurag@Gurome]

Anurag,

Its my mistake.....U had indeed correctly mentioned the solution to be 5...dunno, Y I read 4....

No no. Not yours.
You're correct. I edited that after seeing your post. I thought I had posted a message acknowledging that!