Avisail and Barry drove from Columbus to Des Moines by different route

Question

Avisail and Barry drove from Columbus to Des Moines by different routes, each of which was longer than 900 miles, and neither exceeded the speed limit of 60 miles per hour at any time during their journeys. If they left Columbus at the same time, did Avisail arrive in Des Moines before Barry?

(1) The distance Avisail traveled was 120 miles greater than the distance Barry traveled.

(2) Avisail’s average speed for his trip was 10 miles per hour greater than Barry’s average speed for his trip.

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Vi06 · Accepted Answer

Avisail and Barry drove from Columbus to Des Moines by different routes, each of which was longer than 900 miles, and neither exceeded the speed limit of 60 miles per hour at any time during their journeys. If they left Columbus at the same time, did Avisail arrive in Des Moines before Barry?

(1) The distance Avisail traveled was 120 miles greater than the distance Barry traveled.
 d_A = d_B + 120

(2) Avisail’s average speed for his trip was 10 miles per hour greater than Barry’s average speed for his trip
 s_A = s_B + 10

Avisail's time: t_A = (d_B + 120) / (s_B + 10)
Barry's time: t_B = d_B / s_B

To determine if Avisail arrived first, compare t_A and t_B:
(t_A < t_B) becomes:
(d_B + 120) / (s_B + 10) < d_B / s_B

Cross-multiply:
(d_B + 120) * s_B < d_B * (s_B + 10)

Simplify:
120 * s_B < 10 * d_B
 12 * s_B < d_B (Avisail arrived first if this inequality is satisfied)

Given s_B<60 so 12*s_B(max)< 12*60= 720
But it is also given that distance>900
 Therefore 12 * s_B < d_B (Is not possible hence inequality not satisfied)

Answer -C

itsyodaa · Answer

don't know what is correct option for only statment 1 is correct,, but here 
answer should be statment 1 alone is sufficient to answer the question but statement 2 alone is not sufficient to ans the question

cdrectenwald · Answer

To determine if Avisail arrived before Barry, let's analyze the statements:

(1) Avisail traveled 120 miles more than Barry.
This means Avisail's distance (d_A) is d_B + 120, where d_B is Barry's distance. However, we don't know their speeds, so we can't determine who arrived first. Insufficient.

(2) Avisail's average speed was 10 mph faster than Barry's.
This means Avisail's speed (s_A) is s_B + 10, where s_B is Barry's speed. But we don't know their distances, so we can't calculate who arrived first. Insufficient.

Combining (1) and (2):
We know Avisail's distance is d_B + 120 and his speed is s_B + 10. The travel times are:

Avisail's time: t_A = (d_B + 120) / (s_B + 10)
Barry's time: t_B = d_B / s_B
To determine if Avisail arrived first, compare t_A and t_B:
(t_A < t_B) becomes:
(d_B + 120) / (s_B + 10) < d_B / s_B

Cross-multiply:
(d_B + 120) * s_B < d_B * (s_B + 10)

Simplify:
120 * s_B < 10 * d_B

We still don't know the exact values of s_B or d_B, so we can't determine who arrived first. Even combined, the statements are insufficient.

Answer: E

duyquan2709 · Answer

Yeah, so d_B > 12 s_B and we know that d_b >=900 and s_B<=60 --> 12*s_B<=720 -> answer C

TC97 · Answer

My logic is same as yours. Is E the correct answer?

SohiniRudra · Answer

Why c is correct? the above posts explain whu e is correct but the answer says that c is the right option. can anyone expalin why is that

hr1212 · Answer

Distance travelled by Avisail - Da > 900 and distance travelled by Barry - Db > 900. Also speed of Avisail - Va <= 60 and speed of Barry - Vb <= 60. Is Ta < Tb? Statement 1 - Da = Db + 120 Let's verify with sample values for 2 cases Da Va Ta Db Vb Tb 900 + 120 = 1020 60 17 900 60 15 1020 60 17 900 30 30 As we have insufficient information on the speed we can derive TaTb, hence not sufficient. Statement 2 - Va = Vb + 10 As we don't know anything about the distance travelled, we can similarly conclude that this statement in itself is insufficient as we can get sample cases for both TaTb. Combining both these statements - Now we have some relation between distance and speed to accurately comment on time. Let's try to break down all info we have so far, Da > 900 and Db > 900 Va < 60 and Vb < 60 Da/Ta = Va Db/Tb = Vb Da = Db + 120 Va = Vb + 10 Ta = Da/Va = (Db + 120)/(Vb + 10) Tb = Db/Vb Minimum value of Ta can be obtained when we minimize the numerator and maximize the denominator which would be when Db = 900 and Vb = 50, which would give us Ta = 1020/60 = 17 hrs whereas Tb = 900/50 = 18 hrs, this is the minimum gap between these variables. If we now increase the numerator or decrease the denominator, this gap is always going to increase and in each of these cases Ta < Tb would hold true. Skip fraction breakdown calculation mentioned in spoiler unless someone wants to understand the complexity in detail. Let's break down these fractions - Tb = Db/Vb Ta = Db/(Vb + 10) + 120/(Vb + 10) Min value difference for the first part of this fraction Db/(Vb + 10) to Db/Vb would be when Db is minimized and Vb is maximized which would be 900/60 = 15 to 900/50 = 18. So the minimum difference between Ta and Tb for first part of the fraction can be 3 where Ta < Tb. Min value of the second part of the fraction is when Vb = 50 which gives us 120/(50 + 10) = 2 and this fraction is not present in Tb, so Ta > Tb If we combine these 2 fraction values, we can derive that Ta and Tb can have minimum difference of 1 where Ta < Tb Answer: C

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Avisail and Barry drove from Columbus to Des Moines by different route

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Avisail and Barry drove from Columbus to Des Moines by different route

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