Sebs watch gains 5 seconds in every 3 hours, whereas Lewis watch

Question

Seb’s watch gains 5 seconds in every 3 hours, whereas Lewis’ watch loses 10 seconds in every 2 hours. If both watches are set to the correct time at 1 a.m. Sunday, then at what earliest time they will have a difference of 9 minutes among them?

A 7 a.m. Wednesday
B. 10 a.m. Wednesday
C. 7 p.m. Wednesday
D. 10 p.m. Wednesday
E. 7 a.m. Thursday

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EgmatQuantExpert · Accepted Answer

Solution

Given:  
 • Seb’s watch gains 5 seconds in every 3 hours
• Lewis’ watch loses 10 seconds in every 2 hours
• Both watches are set to the correct time at 1 a.m. Sunday

To find:  
 • At what earliest time the watches will have a difference of 9 minutes among them

Approach and Working:   
 • A difference of 9 minutes is equivalent to 60 x 9 = 540 seconds.

Now, Seb’s watch gains 5 seconds in every 3 hours.
 • Hence, in 1 hour, it will gain  \frac{5}{3}  seconds.

Similarly, Lewis’ watch loses 10 seconds in every 2 hours.
 • Hence, in 1 hour, it will be losing 5 seconds.

• Therefore, in 1-hour time, the difference created between the watches =  \frac{5}{3}  – (-5) =  \frac{20}{3}  seconds

Now, we can say, to create a difference of  \frac{20}{3}  seconds, we need 1 hour.
 • So, to create a difference of 540 seconds, we need 540/( \frac{20}{3} ) = 81 hours.

From 1 a.m. Sunday, 81 hours forward will be 10 a.m. Wednesday.

Hence, the correct answer is option B.

Answer: B

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ankitsaroha · Answer

B

9 minutes = 540 seconds
In every 6 hours, difference increases by 40 seconds.
In 78 hours, by 520 seconds

Only 20 more seconds required.

In next 3 hours, Seb's watch would gain 5 seconds and Lewis's watch would lose 15 seconds (10 seconds in 2 hours is same as 5 seconds in 1 hour)
Difference = 5 + 15 = 20 seconds

Total hours passed = 78+3 = 81
81 hours from 1am Sunday is 10am Wednesday.

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bangu · Answer

9 minutes = 9*60 = 540 seconds.

Seb’s watch gains 5 seconds in every 3 hours
Every hour Seb's match gain 5/3 seconds

Lewis’ watch loses 10 seconds in every 2 hours
Every hour Lewis’ watch loses 10/2 = 5 seconds

Relative difference per hour = 5 + 5/3 = 20/3 Seconds

Time taken to gain 540 seconds = 540/(20/3) = 540*3/20 = 81 hours

81 Hours = 72 Hours (3 24 Hour day) + 9 Hours =>

1 AM + 9 Hours = 10 AM, which is 3 days later i.e. Wednesday.

Option B

harinageshwar · Answer

Hello please help me out.is my approach correct.
3h=> 5sec increase,so
24h=> 40 sec increase.

Similarly 2h=> 10 sec decrease
24hr => 120 sec decrease
So for 48 hrs diff will be =150
72hrs difference will be =240
I am not getting answer like this,
Why this is wrong.

Posted from my mobile device

nishthagupta · Answer

You are wrong because you have assumed that both the increase and decrease are happening over a 2 days , wheras they're actually happening simultaneously.

Regor60 · Answer

The point of this question is that recognizing the least common multiple, 6, simplifies the problem.

Every 6 hrs Seb's watch gains 10 seconds and Lewis's watch loses 30 seconds, for a total difference of:

40s/6 hrs

Since 9 minute difference = 540 seconds, the number of hours required to generate this difference is:

540s/(40s/6hrs) = 13.5*6 =

81 hours.

Since 72 hours = 3 days, 3 days and 9 hours must pass.

So, Wednesday at 10 am

Posted from my mobile device

bumpbot · Answer

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Sebs watch gains 5 seconds in every 3 hours, whereas Lewis watch

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