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siddharthkapoor
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Every day, Tom walks from his home to his office, via the same route, 12 Oct 2019, 06:42
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C
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65% (hard)

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66% (02:48) correct 34% (02:27) wrong based on 489 sessions

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Every day, Tom walks from his home to his office, via the same route, covering s feet at a speed of x feet per minute. Today he took a different route and ended up walking 10% more than he usually does, at a speed of x meters per minute. What is the percentage change in the time he took today compared to the time he takes on a usual day? (1 feet = 0.3 meter)

A. 10% decrease

B. 10% increase

C. 67% decrease

D. 67% increase

E. 200% decrease
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C
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Every day, Tom walks from his home to his office, via the same route, 12 Oct 2019, 19:29
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iamsiddharthkapoor
Every day, Tom walks from his home to his office, via the same route, covering s feet at a speed of x feet per minute. Today he took a different route and ended up walking 10% more than he usually does, at a speed of x meters per minute. What is the percentage change in the time he took today compared to the time he takes on a usual day? (1 feet = 0.3 meter)

A. 10% decrease

B. 10% increase

C. 67% decrease

D. 67% increase

E. 200% decrease

(I) Substitute values for variables..
Let s = 100 and x=10..
Time taken while going 100 at 10 feet per minute= \(\frac{100}{10}=10\) minutes
Time taken on return 1.1*100 at 10 meter per minute or @\(\frac{10}{0.3}\) feet per minute= \(110/\frac{10}{0.3}=\frac{33}{10}=3.3\) minutes

Change or decrease = \(\frac{10-3.3}{10}*100=67\)%

(II) Algebra..
Time taken while going s feet at x feet per minute= \(\frac{s}{x}\) minutes
Time taken on return 1.1*s at x meter per minute or @\(\frac{x}{0.3}\) feet per minute= \(1.1s/\frac{x}{0.3}=\frac{0.33s}{x}\) minutes

Change or decrease = \((\frac{s}{x}-\frac{0.33s}{x})/\frac{s}{x}*100=(1-0.33)*100=67\)%

C
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Every day, Tom walks from his home to his office, via the same route, 13 Oct 2019, 05:29
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let distance s feet = 10feet = 3 mtr
speed = 10 feet per minute ; total time ; 3/10 ; .3 min
new distance ; 3*1.1 ; 3.3 mtrs
speed ; 10/.3 feet per min; time taken ; 3.3/33.33 = .099 min
% ∆ in time = .099-.3/.3 ; (67%)

IMO C


iamsiddharthkapoor
Every day, Tom walks from his home to his office, via the same route, covering s feet at a speed of x feet per minute. Today he took a different route and ended up walking 10% more than he usually does, at a speed of x meters per minute. What is the percentage change in the time he took today compared to the time he takes on a usual day? (1 feet = 0.3 meter)

A. 10% decrease

B. 10% increase

C. 67% decrease

D. 67% increase

E. 200% decrease
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Every day, Tom walks from his home to his office, via the same route, 01 Dec 2020, 20:10
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"Tom ended up walking 10% more" could refer to time or distance, as it is new route...
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Every day, Tom walks from his home to his office, via the same route, 01 Dec 2020, 20:34
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Tigi75
"Tom ended up walking 10% more" could refer to time or distance, as it is new route...


It says walking 10% more than he usually does, and hence it refers to distance.

If it was, taking 10% more than he usually does, then would have referred to time. (In which case the answer would simply have been 10% increase)

Hope this helps

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Every day, Tom walks from his home to his office, via the same route, 24 Jul 2023, 04:08
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siddharthkapoor
Every day, Tom walks from his home to his office, via the same route, covering s feet at a speed of x feet per minute. Today he took a different route and ended up walking 10% more than he usually does, at a speed of x meters per minute. What is the percentage change in the time he took today compared to the time he takes on a usual day? (1 feet = 0.3 meter)

A. 10% decrease
B. 10% increase
C. 67% decrease
D. 67% increase
E. 200% decrease

Old route:

time = distance/rate

time = d/x

New route:

distance = 1.1d

We have to be careful to express the speed in the same unit of measurement:

rate = x m/min = (x m/1 min)(1 ft/0.3 m) = x/0.3 ft/min

time = 1.1d/(x/0.3) = (0.33)(d/x)

new time = (0.33)(old time)

A factor of 0.33 corresponds to a 67% decrease.

Answer: C
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Every day, Tom walks from his home to his office, via the same route, 02 Jan 2025, 13:55
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