Speed&Time

[Akansha]

How long did it take to travel 400km?
a. The car travelled the first 200km in 2.5hrs
b. If the car's average speed had been 20 km/h faster, it would have travelled
the 400km in 1 hour less time.

OA is B

[SoCan]

1) No information on the second 200km. Could have taken any amount of time. Insufficient.
2) Rate*time=400, or r=400/t
(Rate+20)(time-1)=400,
(400/t + 20)(t - 1)=400 ->substituted for r
400 + 20t - 400/t - 20 = 400 -> expand
20t^2 - 20t - 400 = 0 400 on each side cancels, then multiply expression by t
20(t^2 - t - 20) = 0 -> group 20
20(t-5)(t+4) = 0 -> factor
Since time can't be negative, t must equal 5. Sufficient. Answer is B.

[cans]

a) no information about last 200 km and thus insufficient.
b)let initial speed = x and time taken =t
now distance remains same and thus xt=400---- eqn1
also (x+20)*(t-1)=xt => 20t-x-20=0
replace x from eqn1, solve for quadratic in t,
one value will be -ve and as t is time and can't be -ve, reject that value
and the +ve value will be the ans.
Thus sufficient
IMO B