Bob wants to run a mile in the same time as his sister.

Vincen wrote:Bob wants to run a mile in the same time as his sister. If Bob’s time for a mile is currently 10 minutes 40 seconds and his sister’s time is currently 9 minutes 36 seconds, by what percent does Bob need to improve his time in order run a mile in the same time as his sister?

(A) 3%
(B) 5%
(C) 8%
(D) 10%
(E) 12%

The OA is the option D.

What is the equation that I should use here to solve this PS question? I need some help experts. I ask for your help.

We should notice that in this question, “improving the time” means decreasing the time; therefore, we are looking for a percent decrease.

Bob’s time is 10 40/60 = 10 2/3 = 32/3 minutes

His sister’s time is 9 36/60 = 9 6/10 = 9 3/5 = 48/5 minutes

If we let n = the percent less, we have:

(32/3) x (100 - n)/100 = 48/5

(100 - n)/100 = 48/5 x 3/32

(100 - n)/100 = 3/5 x 3/2

(100 - n)/100 = 9/10

100 - n = 90

n = 10%

Alternate Solution:

Bob’s current time is 10 minutes 40 seconds = 640 seconds.

His sister’s current time is 9 minutes 36 seconds = 576 seconds.

Bob must improve his time by 640 - 576 = 64 seconds, and that is an improvement of (64/640) * 100 = 10 percent.

Answer: D