To find the average speed

[gmattesttaker2]

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

[theCodeToGMAT]

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]

[gmattesttaker2]

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

[theCodeToGMAT]

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.

[Stuart@KaplanGMAT]

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

[gmattesttaker2]

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

[gmattesttaker2]

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