Time, Speed and distance 2

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datonman: Senior | Next Rank: 100 Posts; Posts: 53; Joined: Wed May 28, 2014 9:36 pmFollowed by: 1 member

by datonman » Wed Feb 04, 2015 11:49 am

The ratio between the speeds of Mary and Jerry is 7:8 while covering a distance. If Mary takes 20 mins more than Jerry, calculate the time taken by Jerry to cover the distance.

Is there truly a way to solve this by inverting the ratio in regards to time, hence, 7/8 times 8/7?

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Source: Beat The GMAT — Problem Solving | Wed Feb 04, 2015 11:49 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Feb 04, 2015 12:12 pm

datonman wrote:The ratio between the speeds of Mary and Jerry is 7:8 while covering a distance. If Mary takes 20 mins more than Jerry, calculate the time taken by Jerry to cover the distance.

Is there truly a way to solve this by inverting the ratio in regards to time, hence, 7/8 times 8/7?

The RATE RATIO for Mary and jerry is 7:8.
Since rate and time are RECIPROCALS, the TIME RATIO for Mary and Jerry is 8:7.
Implication:
For every 8 minutes that Mary travels, Jerry travels 7 minutes.
Since 8:7 = 80:70 = 160:140, Mary travels for 160 minutes, while Jerry travels for 140 minutes, for a difference of 20 minutes.

Final Answer: 140.

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Thu Feb 05, 2015 9:37 am

datonman wrote:The ratio between the speeds of Mary and Jerry is 7:8 while covering a distance. If Mary takes 20 mins more than Jerry, calculate the time taken by Jerry to cover the distance.

Is there truly a way to solve this by inverting the ratio in regards to time, hence, 7/8 times 8/7?

In the given two cases the constant element is DISTANCE

Distance = Speed x Time

For Mary, Distance = 7a x (t+20) [t is in mins]
For Jerry, Distance = 8a x t

therefore 7a(t+20) = 8at
7t + 140 = 8t
t = 140 mins (Time of Jerry)

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Thu Feb 05, 2015 9:44 am

Another Method:

In the given two cases the constant element is DISTANCE

Distance = Speed x Time

For Jerry, Distance = 8a x t
For Mary, Distance = 7a x (8t/7) [Since distance is constt. therefore if speed becomes 7/8 of previous speed then time will become 8/7 of previous time

and the difference of these times is goven 20 mins

i.e. (8t/7) - t = 20
i.e. t/7 = 20
i.e. t = 140 Mins

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Mon Feb 09, 2015 12:04 am

The crucial insight here is that Mary's Distance = Jerry's Distance. (They both covered "a distance", so it's the same for each of them.) Since Mary's rate and time are given in terms of Jerry's rate and time, we'll assign variables to Jerry, then set Mary's stats in terms of his.

Jerry's R = j
Jerry's T = t

Mary's R = (7/8)j
Mary's T = t + 20

Since their distances are equal, j*t = (7/8)j * (t + 20). Dividing by j, we have t = (7/8)(t + 20), (1/8)t = (140/8), or t = 140.

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