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Difficulty:
55%
(hard)
Question Stats:
70% (03:14) correct
30%
(03:05)
wrong
based on 240
sessions
History
Date
Time
Result
Not Attempted Yet
John leaves Town A. at 12:02 PM and drives to Town B. a distance of 120 miles. His average speed for the first 60 miles was 50 mph and for the final 60 miles it was 40 mph. Jim leaves Town A. at 12:20 PM and also drives to Town B. What must Jim's average speed be in order to arrive at Town B at the same time that John arrives?
A. 35 mph
B. 40 mph
C. 45 mph
D. 50 mph
E. 85 mph
Are You Up For the Challenge: 700 Level Questions
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A. 35 mph
B. 40 mph
C. 45 mph
D. 50 mph
E. 85 mph
Are You Up For the Challenge: 700 Level Questions
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Bryan180599
Joined: 07 Nov 2020
Last visit: 25 Mar 2022
Posts: 10
Location: Belgium
Schools: HEC MFin "23 ESSEC ESCP Europe HEC MiM "25
GMAT 1: 710 Q48 V38
John leaves Town A. at 12:02 PM and drives to Town B. a distance of 120 miles. His average speed for the first 60 miles was 50 mph and for the final 60 miles it was 40 mph. Jim leaves Town A. at 12:20 PM and also drives to Town B. What must Jim's average speed be in order to arrive at Town B at the same time that John arrives?
First I use the formula of speed which is : v = d / t
John makes the first 60 miles at a speed of 50mph. Hence it took him t = d / v. 60/50 =1.2 (so 1 hour and 12 minutes). After that he drove at 40mph, hence t = 60/40 = 1.5 (or 1 hour and 30 minutes). So he arrived at town B at 14h44 (2:44PM)
Jim leaves at 12h20 and must arrive at 14h44. So he must drive 120miles for 2h24 (2.4 in decimal as 24/60 = 0.4). Hence his speed must be v = 120/2.4 = 50
Answer D
First I use the formula of speed which is : v = d / t
John makes the first 60 miles at a speed of 50mph. Hence it took him t = d / v. 60/50 =1.2 (so 1 hour and 12 minutes). After that he drove at 40mph, hence t = 60/40 = 1.5 (or 1 hour and 30 minutes). So he arrived at town B at 14h44 (2:44PM)
Jim leaves at 12h20 and must arrive at 14h44. So he must drive 120miles for 2h24 (2.4 in decimal as 24/60 = 0.4). Hence his speed must be v = 120/2.4 = 50
Answer D
Bunuel
imho not 700-level question
JOHN time 60/50+60/40=1.2+1.5=2.7hrs
2.7hrs=2+7/10*60=2:42
JOHN arrives A-B 14:44
JIM leaves 12:20
JIM must arrive 14:44
2:24hrs=2+24/60=2.4
120/2.4=50
(D)
IMO: D
step 1 - find total time taken by john to reach "B" = (distance1/average speed1)+(distance2/average speed2) =2.7Hr = 14Hr 44 min
step 2 - find the time taken by JIM to reach "B" = 12:20 - 14:44 = 2:24
Step 3 - average speed of JIM = total distance / total time = 120 /(2:24) = 50mph
note - convert 2:24 into hour unit
step 1 - find total time taken by john to reach "B" = (distance1/average speed1)+(distance2/average speed2) =2.7Hr = 14Hr 44 min
step 2 - find the time taken by JIM to reach "B" = 12:20 - 14:44 = 2:24
Step 3 - average speed of JIM = total distance / total time = 120 /(2:24) = 50mph
note - convert 2:24 into hour unit
Not an overly difficult question, but it is time consuming. It's all about setting up the equations.
John's average speed is 50 mph over the first 60 miles and 40mph over the last 60:
Avg1 = 60/t1
50 = 60/t1
t1 = 6/5 h
Avg2 = 60/t2
40 = 60/t2
t2 = 3/2 h
Therefore, the total number of hours spent traveling is 6/5 + 3/2 = 2 and 7/10 of an hour. This means he reached his destination at 2:44 pm.
Since Jim left 18 minutes later at 12:20 pm, that means he has 2 hours and 24 minutes to travel 120 miles
AvgJim = 120/2.4h = 50mph
John's average speed is 50 mph over the first 60 miles and 40mph over the last 60:
Avg1 = 60/t1
50 = 60/t1
t1 = 6/5 h
Avg2 = 60/t2
40 = 60/t2
t2 = 3/2 h
Therefore, the total number of hours spent traveling is 6/5 + 3/2 = 2 and 7/10 of an hour. This means he reached his destination at 2:44 pm.
Since Jim left 18 minutes later at 12:20 pm, that means he has 2 hours and 24 minutes to travel 120 miles
AvgJim = 120/2.4h = 50mph
understanding and solving this question took me long time, especially, took time to find out the time required for Jim...what is the score level of this question (i think it deserve to be at 700 level. any thoughts?
Bunuel
Since distance travelled at two speeds by John is the same, his avg speed will be given by:
Average speed of John = 2ab/(a + b) = 2*50*40/(50 + 40) = 400/9 mph
Time taken by John = 120/(400/9) = 2.7 hrs = 2 hrs 42 mins
Jim starts 18 mins late so needs to complete the same distance in 2 hrs 24 mins = 2.4 hrs
Avg speed of Jim = 120/2.4 = 50 mph
Check:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/0 ... -the-gmat/
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Posts: 67
Hi VeritasKarishma and Bunuel
Greetings of the day.
I have tried to solve this problem but was unable to do so. Then I checked for the available solutions and I found the proper solution. But what I want to ask is, can we solve this problem with Relative speed concept as I was trying this via it and did not get the correct answer. As per my opinion, we can apply that concept in this problem, however, I am not sure where I am going wrong.
Hence, I would request you guys to confirm me whether we can apply Relative speed concept in this problem or not and if yes, then kindly provide solution also, so i can check where i am going wrong.
Many Thanks in advance.
Greetings of the day.
I have tried to solve this problem but was unable to do so. Then I checked for the available solutions and I found the proper solution. But what I want to ask is, can we solve this problem with Relative speed concept as I was trying this via it and did not get the correct answer. As per my opinion, we can apply that concept in this problem, however, I am not sure where I am going wrong.
Hence, I would request you guys to confirm me whether we can apply Relative speed concept in this problem or not and if yes, then kindly provide solution also, so i can check where i am going wrong.
Many Thanks in advance.
RahulHGGmat
John drives at different speeds so using relative speed here will be unnecessarily complicated. It will add no value and we will still need to do everything we are doing right now.
It is a simple average speed question. They both drive independently without reference to the other. We can get the time when John reaches and we need to make Jim reach at the same time so we have distance to be covered and time to be taken. We can easily find his speed.
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