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# How much time does Mr. Richards take to reach his office from home? (1

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Math Expert
Joined: 02 Sep 2009
Posts: 65187
How much time does Mr. Richards take to reach his office from home? (1  [#permalink]

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06 Sep 2019, 09:52
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Difficulty:

95% (hard)

Question Stats:

40% (02:27) correct 60% (02:06) wrong based on 116 sessions

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How much time does Mr. Richards take to reach his office from home?

(1) One day, he started 30 minutes late from home and reached his office 50 minutes late, while driving 25% slower than his regular speed.

(2) He needs to drive at a constant speed of 25 miles per hour to reach his office just in time if he is 30 minutes late from home.

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Joined: 13 Feb 2018
Posts: 18
Re: How much time does Mr. Richards take to reach his office from home? (1  [#permalink]

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07 Sep 2019, 11:30
Bunuel wrote:
How much time does Mr. Richards take to reach his office from home?

(1) One day, he started 30 minutes late from home and reached his office 50 minutes late, while driving 25% slower than his regular speed.

(2) He needs to drive at a constant speed of 25 miles per hour to reach his office just in time if he is 30 minutes late from home.

Tricky question in my opinion.

The fundamental concept here is Velocity = Distance/Time.
So, t = regular time to reach Mr. Richard's house from his house (minutes), d = distance from home to office (miles) and V = regular speed (miles per minutes).

(i) t_initial = 30 and t_final = t + 50.

So, the time requiered is: t_final - t_initial = t +50 - 30 = t + 20.

Also we have V_new = d/(t + 20) --> fundamental relation in the new scenario

On the other hand V_new = 75%*V or 3/4*V, because the velocity is 25% slower than his regular speed

So, V_new = 75%*d/t = d/(t + 20) --> t= 60 Sufficient

(ii) V_new = 25 when t_initial = 30 and t_final = t. So, we have 25 = d/(t - 30). d is unknown, so insufficient

Then the correct answer is (A)

Let me know if you have comments or there is something wrong in my post.

Cheers,
R.
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How much time does Mr. Richards take to reach his office from home? (1  [#permalink]

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07 Sep 2019, 17:23
1
Bunuel wrote:
How much time does Mr. Richards take to reach his office from home?

(1) One day, he started 30 minutes late from home and reached his office 50 minutes late, while driving 25% slower than his regular speed.

(2) He needs to drive at a constant speed of 25 miles per hour to reach his office just in time if he is 30 minutes late from home.

Statement 1:
Mr. Richard takes 20 more min if he drives 25% slower, or at 75% of his regular speed. If he drives at $$\frac{3}{4}$$ of his regular speed, this means he will take $$\frac{4}{3}$$ of his regular time to complete the trip (since distance is fixed). And as we know, he took an extra 20 min, which is the extra $$\frac{1}{3}$$ of his regular time. Therefore his typical driving time is $$20/\frac{1}{3}$$ = 60 min so this statement is sufficient. The key here is that speed and time have an inverse relationship when the distance is fixed. Also, note $$\frac{1}{4}$$ slower speed translates to $$\frac{1}{3}$$ more time used, so we should put these terms in ratios to not confuse ourselves.

Statement 2:
Being 30 min late is not useful information. We only know his speed from this which is insufficient.

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Joined: 11 Feb 2017
Posts: 17
Re: How much time does Mr. Richards take to reach his office from home? (1  [#permalink]

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02 Jun 2020, 23:08
I think this is a question which has one equation and 2 variables and is still solvable,
Bunuel can we please have more of these?
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Joined: 04 Aug 2010
Posts: 663
Schools: Dartmouth College
Re: How much time does Mr. Richards take to reach his office from home? (1  [#permalink]

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03 Jun 2020, 03:07
AabhishekGrover wrote:
I think this is a question which has one equation and 2 variables and is still solvable

Statement 1 does not require two variables.
Rate and time have a RECIPROCAL relationship.
If John works at 3 TIMES his normal rate, he takes $$\frac{1}{3}$$ of his normal time.
If Mary takes $$\frac{1}{2}$$ of her normal time, she travels at TWICE her normal rate.

Statement 1: He started 30 minutes late from home and reached his office 50 minutes late, while driving 25% slower than his regular speed.

Since he travels at $$\frac{3}{4}$$ of his regular speed, he takes $$\frac{4}{3}$$ of his regular time:
$$\frac{4}{3}t$$
Since he starts 30 minutes late but arrives 50 minutes late, he takes 20 minutes longer than his regular time:
$$t + 20$$
The expressions in blue both represent today's time and thus are EQUAL:
$$\frac{4}{3}t = t + 20$$
$$4t = 3t + 60$$
$$t = 60$$
SUFFICIENT
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Re: How much time does Mr. Richards take to reach his office from home? (1   [#permalink] 03 Jun 2020, 03:07

# How much time does Mr. Richards take to reach his office from home? (1

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