Dara ran on a treadmill that had a readout indicating the time remaini

Do a more efficient single calculation:

24 min 18 sec is 90% of her exercise time.
When she completes 40% of her exercise session, the readout will indicate 60% of the time.

So we need \(\frac{6}{9} * 24(\frac{18}{60}) = \frac{81}{5} = 16 ( \frac{1}{5}) = 16 (\frac{12}{60}) =\)16 min 12 sec

*Edited a calculation error.
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90% of the exercise should be completed in 24min 18 sec (1458 sec)

When she completes 40% of her exercise timer should show the time remaining for 60% of her exercise.

If 90% requires 1458 sec then 60% requires --> (60 * 1458)/90 = (2/3)*(1458) = 2 * 486 = 972 secs

Required answer = 972/60 = 16 min 12 sec

Answer: E

We are given that Dara completed 10% of her exercise session when the readout indicated 24 min and 18 seconds as her time remaining. In other words she had 90% left of her workout at that time. We need to determine the readout after she has completed 40% of her exercise, or when she has 60% left.

We can create a proportion to determine the time when Dara has 60% left. First, let’s convert 24 min 18 sec to minutes.

24 min 18 sec = (24 + 18/60) min = (24 + 3/10) min = 24.3 min

We can also express 90 percent as 90/100 = 0.9 and 60 percent as 60/100 = 0.6. We define x as the number of minutes remaining in her workout when she has 60%, or 0.6, of her workout left to do.

Our proportion is as follows:

0.9/24.3 = 0.6/x

9/243 = 0.6/x

9x = 145.8

x = 145.8/9 = 16.2 min

Thus, x = (16 + 2/10) min = (16 + 12/60) min = 16 min 12 sec

Answer: E
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Let's call 24min and 18sec Y.
24min and 18 sec are: 243/10.
Dara completed 10% of her session, so:
243/10 = 9x/10
x=27 min.
27-Y= 2min+42sec
If Dara completed 40% of her session, the she worked for 4*(2min+42sec) so that the rest of her session will be:
27min-10min&48sec = 16 min 12 sec
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24.3 minutes/.9=27 minutes=total time of session
(27)(.6)=16.2 minutes=time remaining when session is 40% completed
16.2 minutes=16 min 12 sec

24 min 18 sec = 1458 sec --> this is 90% of the total workout (w)

.9w = 1458 sec
w = 1620 sec

The readout when she had done 40% of the workout will be 60% of the total

1620*.6 = 972 --> 972/60 = 16 min 12 sec

Answer E

Time remaining when 10% of session completed = 24 mins and 18 seconds.
Let us covert everything in seconds to calculate the total time.

24 mins 18 seconds = 24*60 + 18 = 1440 + 18 = 1458
90% of time = 1458 seconds.

100% of time = 1458*10/9 = 1620 seconds
40% completed = 60% remaining.
Time remaining = 0.6*1620 = 972seconds = 960 + 12 seconds = 16 minutes 12 seconds.

Correct Option: E

I disregarded the minutes and only focused on the seconds since all answer options have a different seconds count.
18 seconds is 90% --> 20 seconds is 100% --> 60% is 12 seconds --> answer E

This problem can be done mentally without any calculations

Readout indicated 24 min 18 sec when she had completed 10% of her exercise.

This means remaining 90% of the work will take 24 min 18 sec => 30% will take 8 min 6 sec

so 40% completed i.e. 60% remaining of the work will take (24min 18 sec- 8 min 6 sec)= 16min 12 sec.
So E is the answer

Although I usually tend to rely on the algebraic approach described for this question by other posters, I want to provide an additional approach.

We are told that 90% of the remaining time equals 24 min and 18 seconds.

We can divide this one 90% portion into three 30% portions:

24 min divided by 3 = 3 portions of 8 min

18 sec divided by 3 = 3 portions of 6 sec

Since 30% + 30% = 60%, we then can make the sum of two of the portions to estimate the remaining time when Dara has completed 40% of the exercise session (or the remaining 60%):

(2 portions of 8 min = 16 min) + (2 portions of 6 sec = 12 sec)

Total = 16 min and 12 sec. Option E.

Hope it helps.

This approach is incorrect, it gives the correct answer out of luck only because the 60% of the total minutes is an integer.

If you want you can separate them, but should be like this:

(1) 24 mins in 90%. Means that in 60%: 60*24/90 = 16 mins (simplify to calculate that)
(2) 18 secs in 90%. Means that in 60%: 60*18/90 = 12 secs (also simplifying)

if (1) turned out to be a fraction, then the answer would not just rely on the 12 secs you calculated.

\(Mental:\)


\(90 percent\) = \(24 min 18 sec\)

\(60 percent\) = \(\frac{2}{3} * 24 min 18 sec\)

= \(16 min 12 sec\), i.e \(\frac{2}{3}\) of each of \(24\) and \(18\) respectively

Hence, E.

Dara passed 10%, so 90% remains ahead of her.
We are asked how much time will remain when she completes 40%, which actually means "how much time will remain when 60% of the run remains ahead of her"?

90% is 9 times 10%, 60% is 6 times 10%, call 10% X. The original time left is 9X, the time left after 40% of the workout is 6X. 6 = 2/3 * 9

If 9X = 24+(18/60):
6X = 2/3 *( 24 + 18/60 ) = 2/3 * 24 + 2/3 *18/60 = 16 + 12/60