Robert and Timothy both left their respective homes at 1 PM. Robert wa

Question

Robert and Timothy both left their respective homes at 1 PM. Robert walked till a lake that was between 2.5 kilometres and 3 kilometres from his home, inclusive, and returned home between 1:55 PM and 2:05 PM. If Timothy walked 5 kilometres more than Robert and returned to her home at 3 PM, which of the following statements must be true?

I. The walking speed of Timothy was greater than that of Robert
II. Robert’s walking speed was close to 3 kilometers per hour
III. Had Robert covered 5 more meters every 18 seconds, his walking speed would have been greater than Timothy’s

A. I only
B. II only
C. III only
D. I, II and III
E. None of the above

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yashikaaggarwal · Answer

Robert and Timothy both left their respective homes at 1 PM.
Robert walked till a lake that was between 2.5 kilometres and 3 kilometres from his home, inclusive, and returned home between 1:55 PM and 2:05 PM.

Additional Information: Timothy walked 5 kilometres more than Robert and returned to her home at 3 PM.

I. The walking speed of Timothy was greater than that of Robert

Let Robert walked the greatest distance at the minimal time.
6km in 55min (3+3 and reached home at 1:55 => 1:55-1:00 => 55min)
Robert speed = 6/(55/60)
=> 6/0.916
=> 6.54km/hour

Since Timothy walk 5 km more than Robert 6+5 = 11 km and reached home in two hours.
=> Timothy speed = 11/2 = 5.5
=> Timothy speed is < Robert (False)

II. Robert’s walking speed was close to 3 kilometers per hour

Let Robert walked the least distance at the greatest time.
5km in 65min (2.5+2.5 and reached home at 2:05 => 2:05-1:00 => 65min)
Robert speed = 5/(65/60)
=> 5/1.083
=> 4.61km/hour (not even near to 3)
(False)

III. Had Robert covered 5 more meters every 18 seconds, his walking speed would have been greater than Timothy’s
=> if Robert walked 5meter at the speed of 18 seconds
5km @5hours (5km = 5000m & 18*1000 = 18000 sec to hours = 18000/3600 = 5 hours)
1km/hour
Average speed = total distance/total time = 5+6 = 11/1.91666 = 5.7km/hour
Since Robert speed is already greater than Timothy. It will be greater than Timothy now too. (True)

Only statement 3 is true

IMO C

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nick1816 · Answer

Range of speed of R is between 5/65 and 6/55 Km/min (both inclusive) or 4.6=< R =<6.5 km/h

speed of T is between 10/120 and 11/120 Km/min (both inclusive) or 5 =< R =< 5.5 km/h

I) R can be greater or less than T
I can be false

Eliminate A and D

II) This option doesn't make sense to me tbh.

4.6 < R < 6.5.

Going with must not be true tho.

III)

new range of the speed of R =  =

range of T =

R will be always greater than T.

Must be true

C

Lipun · Answer

Hi  nick1816  and  Bunuel ,

I solved it using the tedious approach. But I have a few concerns regarding pt II and pt III.

Let distance till lake = L.
2.5 <= L <= 3 => 5 <= 2L <= 6 ----- this is the distance traveled by Rob in time 55 <= T <= 65 mins.

Distance covered by Tim: 10 <= 2L+5 <= 11.
Time taken by Tim: 120 mins

I. The walking speed of Timothy was greater than that of Robert
We need to compare the min speed of Timothy with the max speed of Robert.

Min T = 10/120 = 1/12
Max R = 6/55 ~ 1/9 which is greater than Min T.
So pt 1 is false.

II. Robert’s walking speed was close to 3 kilometers per hour
Min speed of R = 5/(13/12) ~ 5 kmph, greater than 3 kmph. Not close.
But this is very ambiguous because the degree of closeness can't be defined here. For ex, if we compare 3 to 15 and 3 to 5, then 3 to 5 is close.

III. Had Robert covered 5 more meters every 18 seconds, his walking speed would have been greater than Timothy’s
5mt/18s = 1kph.
Let's compare Robert's minimum speed with Timothy's maximum speed.
R's min speed = (5+(13/12))/65 = 73/(12*65) ~ 1/11
T's max speed = 11/120 ~ 1/12 which is less than R's speed of 1/11. So, pt 3 is always true.

However, the exact value of R(min) = 0.093 and T(max) = 0.091. When the exact values are this close, rounding even a single unit can in turn return the wrong result. But calculating these values are not possible in the time frame of GMAT.

Kindly suggest what is the best suited approach to such questions.

Regards
Lipun

rajeshforyouu · Answer

R ----------------LAKE  ------------------------  T

R: Robert's home
T: Timothy's home
& there is a lake in between

Let's take extreme conditions

Robert walked till the Lake (3 km) & came back in 1 hr (1 PM - 2 PM)
Basically he moved from R to Lake & then Lake to R. So either way he'll cover same distance.

R to Lake: 3km - 30mins
Lake to R: 3km - 30mins

So  Robert's speed is 6 km/hr

Now Timothy covered 5 kms more than Robert i.e 6 + 5 = 11 kms & took 2 hrs (1 PM - 3PM)

T to Lake: 5.5 km - 1 hr
Lake to T: 5.5 km - 1 hr

So  Timothy's Speed is 5.5 km/hr

I.   False

Timothy's Speed : 5.5 km/hr
Robert's speed : 6 km/hr

II.   False

Robert's speed : 6 km/hr

III.   True

Robert's Speed is already more than Timothy's.
Robert now covers +5 m in 18 secs. So in 1 hr (3600 seconds) he will cover 3600*5/18 = 1000 m = +1 km

Robert's speed becomes 6+1 = 7 km/hr
Timothy's Speed is 5.5 km/hr

nick1816 · Answer

Lipun

You're correct about statement II. I found it ambiguous too.

Statement III is pretty much straightforward , i guess. You should consider their speed in Km/h (you already have calculated that for statement II). It would make calculation much easier. Adding 1 km/h in the minimum possible speed of R makes it greater than max possible speed of T. Hence, III must be true for all values of R and T.

Lipun · Answer

Thank you for your response nick1816 .

I guess I was making it overly complicated by taking exact values (55 secs and 65 secs). Best to approximate such questions I think. Saves hell lot of time. Best Regards Lipun

ScottTargetTestPrep · Answer

Solution:

Notice that Robert walked between 2 x 2.5 = 5 km and 2 x 3 = 6 km in 55 minutes to 65 minutes.

If Robert walked 5 km in 65 minutes, his speed was roughly 4.61 km/h. If, on the other hand, Robert walked 6 km in 55 minutes, his speed was roughly 6.55 km/h. His actual speed could have been anything between 4.61 and 6.55 kilometers per hour.

Assume Robert walked 6 km in 55 minutes. Then, Timothy walked 6 + 5 = 11 km in 2 hours. Thus, the speed of Timothy was 11/2 = 5.5 km/h, which is less than 6.55. Thus, statement I is not necessarily true.

We found that Robert’s speed was between 4.61 and 6.55 km/h. Since the lower end of Robert’s speed was 50% more than 3 km/h and his actual speed was even more than that, statement II is false.

Finally, 5 more meters every 18 seconds is the same thing as 5 x 200 more meters in 18 x 200 = 3,600 seconds = 1 hour. Thus, 5 more meters in 18 seconds means 1,000 meters = 1 kilometer more distance traveled; thus the speed would have been exactly 1 km/h greater. Under this assumption, Robert’s speed was between 4.61 + 1 = 5.61 km/h and 6.55 + 1 = 7.55 km/h.

We found that the fastest Timothy could ever walk was if he walked 11 km in 2 hours; i.e. a speed of 5.5 km/h. We see that even if Timothy walked the fastest he could, he could not walk as fast as Robert’s slowest possible speed. Thus, statement III is true.

Answer: C

Robert and Timothy both left their respective homes at 1 PM. Robert wa

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