Edited) Don completes a car journey totalling x miles.

Question

(Edited) Don completes a car journey totalling x miles. During 5 miles of the journey his average speed is 30 miles per hour. For the rest of the journey his average speed is 60 miles per hour. His travel time for the x mile trip is what percent greater than if he'd travelled the whole distance at 60 miles per hour.

a) 8.5%

b) 50%

c) (x/12)%

d) (60/x)%

e) (500/x)%

MBAlad · Answer

Every time I work it out I always end up with 500/x + 100?

MBAlad · Answer

I got it!! Albeit in slightly over 2 mins. Mistake I was making is what % greater is the journey and so was forgetting to take away 100.

Nsentra · Answer

Could you show me where I went wrong?

  / Xmi/60mph

so I get 55/60 * 60/x = 55/x*100 = 550/x%

heman · Answer

I am getting 5500/x % ??

Broken journey time = 1hr + x-5/60
= x+55/60

One shot journey time= x/60

% inc = (x+55 - x)/60 * 60/x * 100%
 = 55/60 * 60/x *100
= 5500/x % ??

Heman

smily_buddy · Answer

Shouldn't this be 5500/x% and this is not any part of the answer???

Nsentra · Answer

oops, you're right. but I know it wasn't correct, I was asking MBAlad to show us his math.

paddyboy · Answer

Ditto <img src="{SMILIES_PATH}/icon_rolleyes.gif" alt=":roll:" title="Rolling Eyes" />

MBAlad · Answer

working is as follows:

speed = distance/ time ----> Time = distance over speed

time for portion of journey travelling at 30mph = 5/30 or 10/60

time for rest of journey at 60mph = (x-5)/60

time for journey travelled entirely at 60mph = x/60

total time for journey with mixed speed = 10/60 + (x-5)/60

= x+5/60

Now we need to divide this by x/60 (or multiply by 60/x) to give us the fraction of the journey time at x/60

---> 60(x+5)/60x

Cancelling out ---> x+5/x which can be reduced to (5/x) + 1

Multiply by 100 to give percentage = (500/x) + 100

Subtract 100 to give percentage change

----> 500/x %

Mistake I was making was to not subtract 100 to give %  change

paddyboy · Answer

30mph?!

The question sez 5!

MBAlad · Answer

Apologies guys - is meant to read 30mph

Nsentra · Answer

<img src="{SMILIES_PATH}/1done.gif" alt=":done" title="Done" />

cicerone · Answer

Folks, I don't find this tough.
Use the loophole of the given problem.
Clearly the answer is dependent on x. So options a and b are out.
Any way what i say here is take a value for x and proceed.
Let's take x= 20.

Initially 5 miles is travelled with 30mph. So time taken is 5/30 = 1/6 of hour = 10 minutes.

Remaining 15 is travelled with 60mph. So time taken is 15/60 = 1/4 of hour = 15 minutes.

So total time taken is 25 minutes.

In the second case entire 20 is travelled with 60 mph.
So time taken is 20/60 = 1/3 of hour = 20 minutes.

So times taken are 20 and 25 minutes respectively.
Clearly time taken in the first case is 25% more than the later case.

Now placing x=20, option E gives us 25%.

So the answer is E.

Is this clear?

Regards,

necromonger · Answer

*chuckle* No.6, the Twister. https://www.gmatclub.com/phpbb/viewtopic.php?t=34329 :) be careful of these questions!!

MBAlad · Answer

You mean E)

60/20 = 3

500/20 = 25

MBAlad · Answer

Necromonger, I happened to read your post yesterday and thought of this question.

Great website!

necromonger · Answer

Thanks, glad you found it useful.

lfox2 · Answer

I think that 2 of the answers are correct (depending on what x is)

For example, if X = 10 miles, then the first 5 miles will take 12 mins at 30mph. Then the next 5 miles will take 6 mins at 60mph. Total journey time will take 18mins.

If the 10 miles are driven at 60mph then it will take 12mins.

So the answer is that it will take an additonal 6mins driving at 30mph and then at 60mph.

This is a 50% increase on the 12mins. That means B is the correct answer. If you then place x into the answer E, it also works.

What do you think?

Edited) Don completes a car journey totalling x miles.

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