To find the average speed

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Mon Dec 23, 2013 11:04 pm

Hello,

Can you please assist with this:

If it took a sports car and a truck the same time to travel distances of 120 and 100
miles, respectively, what was the average speed of the truck?

(1) It took the car 30 minutes to travel half of the distance.

(2) The average speed of the truck was ten miles per hour less than the average speed of
the car.

OA: B

I am trying to solve as follows:

Since it took the sports car and the truck the same time to travel distances of 120 and 100, let the time be "t"

Rate x Time = Distance
r1 x t = 120 (For Sports car)
r2 x t = 100 (For truck)

We need to find r2.

Statement 1 says it took the car 30 minutes to travel half of the distance
=> 1 hour to travel the entire distance
=> t = 1 hour

Hence, r2 x 1 = 100
=> r2 = 100 m/hr

Sufficient.

Statement 2 says that the average speed of the truck was ten
miles per hour less than the average speed of the car.

Rate x Time = Distance
r1 x t = 120 (For Sports car)
r2 x t = 100 (For truck)

Given, r2 = r1 - 10
Hence,
r1 x t = 120 (For Sports car)
(r1 - 10) x t = 100 (For truck)

Solving we get t = 2 hours
Hence, r2 x 2 = 100 (for truck)
=> r2 = 50

I was not sure if I was solving this correctly since I am getting different values for r2 in I and II. Can you please assist?

Thanks,
Sri

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 23, 2013 11:04 pm

theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Mon Dec 23, 2013 11:23 pm

Time of Sports Car = Time of Truck
120/S = 100/T
T/S = 5/6 -(1)

To find: T

Statement 1:
Distance = 60
Time = 0.5 hours
Speed for first Half = 60/0.5
BUT, we have no info about total time
INSUFFiCIENT

Statement 2:
T = S - 10
S = T+10
using in (1)
T/(T+10) = 5/6
We can solve and get "T"
SUFFICIENT
Answer [spoiler]{B}[/spoiler]

R A H U L

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Mon Dec 23, 2013 11:54 pm

theCodeToGMAT wrote:Time of Sports Car = Time of Truck
120/S = 100/T
T/S = 5/6 -(1)

To find: T

Statement 1:
Distance = 60
Time = 0.5 hours
Speed for first Half = 60/0.5
BUT, we have no info about total time
INSUFFiCIENT

Statement 2:
T = S - 10
S = T+10
using in (1)
T/(T+10) = 5/6
We can solve and get "T"
SUFFICIENT
Answer [spoiler]{B}[/spoiler]

Hi,

Thanks for your reply. I had the following question about Statement I.

Since rate is 60/0.5 miles/hour and distance is 120 miles, cannot we not calculate the time ?

Thanks,
Sri

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Tue Dec 24, 2013 12:24 am

gmattesttaker2 wrote: Hi,

Thanks for your reply. I had the following question about Statement I.

Since rate is 60/0.5 miles/hour and distance is 120 miles, cannot we not calculate the time ?

Thanks,
Sri

If we solve 60/0.5 = 120.. then we get the speed for the first half distance but we don't know, for the rest half distance, the time Truck/Car consumed; we cannot extrapolate to conclude that for rest half also it took 30 minutes..
That's why Statement 1 is Insufficient.

R A H U L

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Tue Dec 24, 2013 12:32 am

Sri wrote:Hi,

Thanks for your reply. I had the following question about Statement I.

Since rate is 60/0.5 miles/hour and distance is 120 miles, cannot we not calculate the time ?

Thanks,
Sri

Hi Sri!

You've assumed that the car's speed is constant - which is exactly what the question is designed to trick you into assuming!

Remember: on the GMAT we only know what we're explicitly told. Since we don't know whether the car is travelling at a constant speed, there's no way we can determine how long the other half of the trip took it.

Here's the good news - you fell for the trap in practice, so you won't fall for it on the actual test!

Stuart

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Tue Dec 24, 2013 10:47 am

theCodeToGMAT wrote:
gmattesttaker2 wrote: Hi,

Thanks for your reply. I had the following question about Statement I.

Since rate is 60/0.5 miles/hour and distance is 120 miles, cannot we not calculate the time ?

Thanks,
Sri
If we solve 60/0.5 = 120.. then we get the speed for the first half distance but we don't know, for the rest half distance, the time Truck/Car consumed; we cannot extrapolate to conclude that for rest half also it took 30 minutes..
That's why Statement 1 is Insufficient.

Hello,

Thank you very much for clarifying.

Best Regards,
Sri

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Tue Dec 24, 2013 10:58 am

Stuart Kovinsky wrote:
Sri wrote:Hi,

Thanks for your reply. I had the following question about Statement I.

Since rate is 60/0.5 miles/hour and distance is 120 miles, cannot we not calculate the time ?

Thanks,
Sri
Hi Sri!

You've assumed that the car's speed is constant - which is exactly what the question is designed to trick you into assuming!

Remember: on the GMAT we only know what we're explicitly told. Since we don't know whether the car is travelling at a constant speed, there's no way we can determine how long the other half of the trip took it.

Here's the good news - you fell for the trap in practice, so you won't fall for it on the actual test!

Stuart

Hello Stuart,

Thank you very much for clarifying and for the tip.

Best Regards,
Sri

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