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

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

My logic is same as yours. Is E the correct 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

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

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 Ta<Tb or Ta>Tb, 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 Ta<Tb and Ta>Tb.

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.


Answer: C