the destination of Donald?

[sanju09]

Donald is driving at a given speed, which if quartered; it would take him 3 hours longer to reach the destination than what is the normal time. How long in miles is the destination of Donald?
(1) It would take Donald 1 hour to reach his destination if he drives at the given speed.
(2) The difference in the given and the quartered speeds of Donald is 60 miles per hour.

Made Up

[Bill@VeritasPrep]

Donald is driving at a given speed, which if quartered; it would take him 3 hours longer to reach the destination than what is the normal time. How long in miles is the destination of Donald?
(1) It would take Donald 1 hour to reach his destination if he drives at the given speed.
(2) The difference in the given and the quartered speeds of Donald is 60 miles per hour.

Made Up

From the stem:

Normal speed:

D=RT

Reduced speed:

D=(R/4)(T+3)

D=(RT+3R)/4

4D=RT + 3R

4D - 3R = RT

Plug into the normal speed equation:

D = 4D - 3R

3D = 3R

D = R

Statement 1 tells us that T = 1, so in D=RT, D=R, which we already knew from the question stem. No new info means it's not sufficient, so eliminate A and D, and you can also eliminate C because adding it to Statement 2 won't help.

Statement 2 tells us that R - R/4 = 60, which we can solve:

R - R/4 = 60

4R/4 - R/4 = 60

3R/4 = 60

3R = 240

R=80

Since we know that D = R, then D = 80 as well. Sufficient.


B

[sanju09]

Donald is driving at a given speed, which if quartered; it would take him 3 hours longer to reach the destination than what is the normal time. How long in miles is the destination of Donald?
(1) It would take Donald 1 hour to reach his destination if he drives at the given speed.
(2) The difference in the given and the quartered speeds of Donald is 60 miles per hour.

Made Up

From the stem:

Normal speed:

D=RT

Reduced speed:

D=(R/4)(T+3)

D=(RT+3R)/4

4D=RT + 3R

4D - 3R = RT

Plug into the normal speed equation:

D = 4D - 3R

3D = 3R

D = R

Statement 1 tells us that T = 1, so in D=RT, D=R, which we already knew from the question stem. No new info means it's not sufficient, so eliminate A and D, and you can also eliminate C because adding it to Statement 2 won't help.

Statement 2 tells us that R - R/4 = 60, which we can solve:

R - R/4 = 60

4R/4 - R/4 = 60

3R/4 = 60

3R = 240

R=80

Since we know that D = R, then D = 80 as well. Sufficient.


B

Perfect! Looking for a shorter elucidation.