How much time did it take a certain car to travel 400 kilometres?

(1) The car traveled the first 200 kilometers in 2.5 hours.
(2) If the car's average speed had been 20 kilometers per hour greater than it was, it would have traveled the 400 kilometers in 1 hour less time than it did.



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Distance: 400
Speed: x
Time:

= + 1

Now solve:








so X is equal to 80 or -100. Obviously he can't be going -100km/h, so x = 80kmh.

Test it out:



and



Answer B

Hope that helps

to eliminate the denominators I multiplied each term by x(x+20). Some of the terms canceled out, such as 400/x * x(x+20) where the x cancels out and we're left with 400(x+20)

1) Insufficient
We dont know the average speed. Hence the time, spent in first 200 km does not make any sense.

2) Sufficient
vt = 400 -------(1)

vt = 200 = (v+ 20) (t - 1)

vt = vt + 20t - v - 20
20t = v + 20

Multiply both sides by t
20t^2 = vt + 20t
20t^2 = 400 + 20t -----(we know vt = 400)
t^2 = 20 + t

hence t^2 - t - 20 = 0

This will gives us two roots one positive and one negative. Hence t has unique value. Sufficient

hence B

Please post it in data sufficiency section.this is problem solving thread.

Posted from my mobile device

How much time did it take a certain car to travel 400 kilometres?

Let the average speed of the car be \(s\) km/h and the time it spent to cover 400 km be \(t\) hours, then \(st=400\) (\(s=\frac{400}{t}\)). Question: \(t=?\)

(1) The car traveled the first 200 km in 2.5 hours --> we don't know the time the car needed to travel the second 200 km, so this statement is clearly insufficient.

(2) If the car's average speed had been 20km per hour greater than it was, it would have traveled the 400km in 1 hour less than it did --> \((s+20)(t-1)=400\) --> \(st-s+20t-20=400\) --> as \(st=400\) and \(s=\frac{400}{t}\) --> \(400-\frac{400}{t}+20t-20=400\) --> 400 cancels out and after simplification we'll get: \(20t^2-20t-400=0\) --> \(t^2-t-20=0\) --> \((t-5)(t+4)=0\) --> \(t=5\) or \(t=-4\) (not a valid solution as time can not be negative), so \(t=5\). Sufficient.

Answer: B.

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