City A and City B are located 610 kilometers (km) apart from each oth

Question

﻿City A and City B are located 610 kilometers (km) apart from each other on Highway X. At 8:00 a.m., Alonzo began driving along Highway X from City A to City B at an average driving speed of 90 kilometers per hour (km/h). At 9:30 a.m., on the same day, Ryan began driving along Highway X from City B to City A at an average driving speed of 100 km/h. How long, in hours and minutes to the nearest minute, did Ryan drive before meeting Alonzo on Highway X ?

A. 2 hours 30 minutes
B. 2 hours 50 minutes
C. 3 hours 13 minutes
D. 3 hours 55 minutes
E. 4 hours 0 minutes

JeffTargetTestPrep · Accepted Answer

Alonzo (from A to B):

Since Alonzo began driving 1.5 hours earlier than Ryan, Alonzo drove 1.5 hours more than Ryan until they met.

rate = 90 km/h
time = t + 1.5 h
distance = rate × time = 90(t +1.5) = 90t + 135 km

Ryan (from B to A):

rate = 100 km/h
time = t h
distance = rate × time = 100t km

Until they met:

distance₁ + distance₂ = total distance

90t + 135 + 100t = 610
190t = 475

t = 475/190 = 95/38 = 5/2 h = 2 h 30 min

Answer: A

Paras96 · Answer

City A and City B are located 610 kilometers (km) apart from each other on Highway X. At 8:00 a.m., Alonzo began driving along Highway X from City A to City B at an average driving speed of 90 kilometers per hour (km/h). At 9:30 a.m., on the same day, Ryan began driving along Highway X from City B to City A at an average driving speed of 100 km/h. How long, in hours and minutes to the nearest minute, did Ryan drive before meeting Alonzo on Highway X ?

Distance travelled by Alonzo from 8 am to 9:30 am => 90 * 1.5 = 135 Km
Distance left to travelled by Alonzo = 610-135=475

Meeting time = Distance left/Relative velocity= 475/(100+90)=475/190=2.5 hours = 2 hours 30 minutes

therefore A

Distance travelled by Alonzo from 8 am to 9:30 am => 90 * 1.5 = 135 Km
Distance left to travelled by Alonzo = 610-135=475

Meeting time = Distance left/Relative velocity= 475/(100+90)=475/190=2.5 hours = 2 hours 30 minutes

therefore A

gmatophobia · Answer

Between 8:30 am and 9:00 am  : Distance covered by Alonzo between 8:00 am and 9:30 am = 1.5 * 90 = 90 + 45 = 135 kms

At 9:30 am  : Distance between Alonzo and Ryan = 610 - 135 = 475 kms

The ratio of distance covered when they meet will be in the ratio of their speed

Speed of Ryan / Speed of Alonzo =  \frac{100}{90} = \frac{10}{9}

Therefore Ryan covers 10 out of 19 parts, and Alonzo covers the remaining 9.

Value of each of the 19 parts =  \frac{475 }{ 19} = 25

Distance covered by Ryan =  10 * 25

Speed of Ryan =  100

Time taken =  \frac{250}{100} = 2.5  hours

Option A

Archit3110 · Answer

we know that Alonzo had a head start of 90 mins so distance travelled in this duration will be 
90/60 * 90 ; 135 km
net distance between Alonzo and Ryan now is 610-135 ; 475
since they are moving in opposite direction so relative speed is 190 kmph
time they will meet is 475/190 ; 2hrs 30 mins
option A

DanTheGMATMan · Answer

Classic convergence problem- check out this solution:
 https://www.youtube.com/watch?v=I_AUtpDVssU

Sahil_Garg · Answer

(t+1.5)*90 + 100t = 610

90t + 135 + 100t = 610

190t = 475

t = 2.5 hrs

quosrecusandae · Answer

To simplify further, we can do it in a non heavy calculated way

Distance between two points = 610
Speed of first guy = 90
Speed of second = 100

Hour | First | Second

1 | 90 | 610
2 | 180 | 560 (50 miles because he started at half of this hour, which means, he travels only 50 miles this hour)
3 | 270 | 460
4 | 360 | 360

And Voila, we have our answer

At hour 4, considering that second person started at hour 1.5, our answer becomes 4 - 1.5 = 2.5

City A and City B are located 610 kilometers (km) apart from each oth

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GMAT Problem Solving (PS) Questions

City A and City B are located 610 kilometers (km) apart from each oth

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards