A car travels from city a to city B, a distance of 240kms. T

Question

A car travels from city a to city B, a distance of 240kms. The car travels half the distance at x kmph and the remaining distance at x+20 kmph. If the car has to complete the journey in less than 5 hours what should be the minimum value of x?

No options given

Ans: 40

Please explain

a) 20
b) 30
c) 40
d) 50
e) 60

No options were given. This question was given for conceptual understanding and it came with no options. For the sake of the reader, I am making my own optionsl

Source:4gmat

WoundedTiger · Answer

Welcome to Gmat Club!! Please post your question with source and answer options. All PS question on GMAT have 5 options in ascending or descending order... Some links which will help you navigate through gmatclub.. rules-for-posting-please-read-this-before-posting-133935.html all-you-need-for-quant-140445.html gmat-prep-software-analysis-and-what-if-scenarios-146146.html#p1171760 As for the options x will have to be more than 40 km/hrs since the time taken to cover this distance is less than 5 hrs but if speed is 40km/hr then time required will be equal to 5 hrs...

smyarga · Answer

To have the minimum value of speed you need the maximum possible time. So, the time is 5.
Just fill the rate table and use that 
rate*time=distance

_______________rate_______time_________distance
first half________x________120/x_________120
second half____x+20____120/(x+20)_____120
Total______________________5_____________240

So, we have the equation:
 \frac{120}{x}+\frac{120}{x+20}=5

On GMAT it is better here to to plug in the answers.

Divide by 120
 \frac{1}{x}+\frac{1}{x+20}=\frac{5}{120} 
Common denominator
 \frac{2x+20}{x(x+20)}=\frac{1}{24} 
Cross multiply
 48x+480=x^2+20x 
 x^2-28x-480=0 
Viet's theorem
 x=40  or  x=-12 
So, the speed is 40.

Don't really know how to solve this equation faster.

WoundedTiger · Answer

Hi smyarga,

At x=40, the time required will be 5 hrs so speed should be more than that..am I correct ...I did solve the problem like you did and got x=40

Posted from my mobile device

smyarga · Answer

You are right! That's why a wrote that to have minimum speed you need maximum possible time:) because if you go faster, you will come earlier)

SunthoshiTejaswi · Answer

THEY HAVE TOLD THEY HAVE TO COMPLETE THE JOURNEY IN LESS THAN 5 HOURS THEN HOW CAN IT BE EQUAL TO 5/
?

roopika2990 · Answer

Yes .. which is why the answer should be 50 from the options given .. the actual answer should be a non terminating decimal 40.000000........1

rhine29388 · Answer

I have encountered a problem with solution of this problem. the correct answer is option C - 40 kmph . but if we take the value and solve for
120/x + 120/(x+20) = 5
we get that journey is completed in exactly 5 hrs
But as mentioned in question stem journey is to be completed in less than 5 hours value of correct x should be a bit more than 40.
it can be 40.001 or 41 or 45 or any value>40
So the correct answer appears to be flawed

Mahesh41285 · Answer

less than 5 hours not equal to five hours

pushpitkc · Answer

Hi  Bunuel

This question has an OA which does not match the wording. If I am not wrong,
the answer to this question cannot be 40 km/hr!

At a speed of 40 km/hr, the car would travel 120 km (half the distance) in 3 hours 
and the travels the remainder of the distance, traveling at 60 km/hr, in 2 hours.
The total time taken is 5 hours! But as it is explicitly stated in the question, the car
must complete the journey in less than 5 hours. IMO, the OA must be changed!

A car travels from city a to city B, a distance of 240kms. T

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