Andy and Frank start out at opposite ends of a 450-mile route, cycling : Two-part Analysis (TPA)

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Mathivanan Palraj

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16 Apr 2016, 01:46

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Nevernevergiveup

Source: Veritas prep

Andy and Frank start out at opposite ends of a 450-mile route, cycling toward each other at their respective constant rates. Frank cycles at 15 miles per hour and Andy cycles at 25 miles per hour. If Andy leaves at 6am and Frank leaves at some point after that, which combination below represents a time at which Frank begins his ride and a time at which the two will meet along the route?

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Solution

For a question like this, it can be helpful to set up your own grid, noting the times that Frank can leave, the distance Andy will have traveled at that point,the distance they'll need to cover together, and the time at which they'll have covered that distance (working at their combined rate of 40 miles per hour):

Frank Leaves.....Andy Has Traveled......Distance Remaining....Time They Meet

8am..........50 miles.....400 miles......6:00pm

10am........100 miles......350 miles.......6:45

12pm........150 miles......300 miles......7:30

This row is reflected in two answer choices, so it's the correct pairing of 12pm and 7:30pm.

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Here is a better solution. IR questions are usually time consuming if you dont know where to start.

Let t be the time after which Andy and Frank meet and x be the number of hours AFTER 't', when Frank starts.

Thus, per the question,

15*(t-x)+25*t = 450 ---> t = (90+3x)/8, realize that the options given are either complete hours or half hours.

Thus, the value of x will be such that it gives a value of t as a.0 or a.5 hours (i.e. divisible by 4 but NOT by 8).

Use the options to see what values of x you need,

Start with x= 2 (for 8 am), x = 3 for 9 am, x= 4 for 10 am , x = 6 for 12 PM etc.

You will see that when x =6 (i.e. Frank starts at 6 AM+ 6 hours = 12 PM), t = 13.5 hours from 6 am --> 7:30 PM.

Thus, your values are 12 PM and 7:30 PM.

Hope this helps.

1.The table contains three columns and the third column heading is not defined.
2.The problems describes a word 'combination' and each row of the table contains only one value.
3.Therefore, the problem is not comprehensible.

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16 Apr 2016, 05:12

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Mathivanan Palraj

The question is completely fine. This is what you will get in IR in GMAT (this question is a type of 2 part IR question). The question says "which combination below represents a time at which Frank begins his ride and a time at which the two will meet along the route?" You thus have to find a combination of times (a,b) such that a represents the time at which Frank begins his ride and b represents a time at which the two will meet along the route. Just saying that the 'problem is not comprehensible' is not going to be enough on GMAT.

3rd column already has am and pm next to the numbers. So this column can only represent time in a give day.

FYI, the correct set of times for this question is (12, 7:30) such that Frank started at 12 PM and they met at 7:30 PM.

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SohamS

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30 Dec 2020, 06:06

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What am i missing here?
Total D = 450miles
Andy starts at 6am at 25mph and Frank at x hours after 6am at 15 mph
So, in x hours, andy has travelled 25x miles

So the total distance left = 450 - 25x

Let the time they require to meet each other be y hours
therefore, y = (450-2x)/25+15. therefore we have 2 solutions (x = 2 & y = 10 and x = 10 & y = 5)

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15 Jun 2024, 09:17

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abhimahna But how did you figure out all on a sudden that frank started out at 12 pm ?
KarishmaB chetan2u GMATinsight Any cool idea as to how to figure out which number to pick ?

abhimahna

The best way to solve this question to to solve using answer choices.

If I take Frank starts at 12 noon, then Andy waould have travelled 25*6=150 miles.

Thus Gap between the two is 450-150=300 miles.

Time taken to meet = Gap/Sum of speeds ( Sum is taken because they are travelling in opposite directions)

=> Time taken = 300/25+15=7.5 hours.

Thus, after 12 noon, they will take another 7.5 hours to meet. Hence answer is 7:30 p.m. for them to meet.

Thus, 12 and 7:30 is the correct combination.

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02 Jul 2025, 14:09

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you guess and check rather than creating an system.
Plugging in the answer choices goes quicker than creating a table with multiple equations.
Even if you don't initially pick the right answer choice, you can rule them out until you find the right one.

sayan640

abhimahna But how did you figure out all on a sudden that frank started out at 12 pm ?
KarishmaB chetan2u GMATinsight Any cool idea as to how to figure out which number to pick ?

abhimahna