Elena cycled a charity route at a constant speed. How many hours did

Question

Elena cycled a charity route at a constant speed. How many hours did it take Elena to complete the route?

(1) If Elena had cycled 6 kilometers per hour faster than she actually did, she would have completed the route in 3 hours 45 minutes.
(2) If Elena had cycled 25 percent faster than she actually did, she would have completed the route in 4 hours.

thisisakr · Accepted Answer

So the question gives one information that speed is constant.

We know that Speed * Time = Distance or d=st

Let’s start with 2nd statement

Assume initial Speed s , time taken t and distance travelled d
So d=st ———— A

Now question says if speed was 25% more time taken would be 4hrs 
So new speed = 1.25 s
t=4hrs
Distance d remains same so d= 1.25 s * 4 ——— B

Equating eq. A and B as d is same

st = ( 1.25 * 4 )s 
t= 1.25*4=5 hrs 
So this is  Sufficient

Now first statement says if the speed was 6kmph more time taken would be 3hrs 45 mins

New speed = s+6 
Time t = 3.75 hrs 
d= (s+6) * 3.75
Equating it to initial distance d=st
st= s+6 * 3.75

We can’t find t with this so it’s  insufficient

Hence answer is B

Bunuel · Answer

GMAT Club Official Solution:

Elena cycled a charity route at a constant speed. How many hours did it take Elena to complete the route?

(1) If Elena had cycled 6 kilometers per hour faster than she actually did, she would have completed the route in 3 hours 45 minutes.

Let Elena’s actual speed be v km/h and the route length be D km. This statement gives D = (v + 6) * 3.75. The actual time is D/v = 3.75 * (v + 6)/v, which depends on v. Not sufficient.

(2) If Elena had cycled 25 percent faster than she actually did, she would have completed the route in 4 hours.

If her speed were 25 percent greater, it would be 1.25v. This statement gives D = 1.25v * 4 = 5v, so the actual time is D/v = 5 hours. Sufficient.

Answer: B.

prateekthechaser · Answer

As we does not have speed and distance so we cannot calculate the time in A. But we know there is a inverse relation between speed and time so as speed increased by 25% time will be reduced by 20% and 4 hours is 80% time so we can easily calculate time. Answer is B

Adit_ · Answer

D = ST and here only statement 2 states that one is a multiple of another in which case the variables for speed get cancelled out and can solve for time.
Statement 1 does not let the variable speed get cancelled out.

Answer:  Option B

vitaeveritatis · Answer

Statement 1:

Let initial speed be (s1)= xkm/hr
New Speed = (x+6) km/hr

Distance = speed x time

D = (x+6)x3.75 As new time given - 3 hrs 45 mins or 3+45/60 =3.75 hrs

Therefore t1 = d/s1
t1=((x+6)x3.75)/x

where t1 can't be determined ,hence Statement 1 is insufficient alone.

Statement 2 :

Initial speed - x km/hr
New Speed (s2) - 5x/4 km/hr

Distance = 5x/4 x 4 = 5x km

therefore original time = 5x/x = 5 hrs

Statement 2 alone is sufficient .

Ans - Option B

Elena cycled a charity route at a constant speed. How many hours did

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GMAT Data Sufficiency (DS) Questions

Elena cycled a charity route at a constant speed. How many hours did

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