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# If Robin drives at 20 kilometer per hour, she reaches office at 3 pm.

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Re: If Robin drives at 20 kilometer per hour, she reaches office at 3 pm. [#permalink]
Hi,
I have taken the following approach to solve this question. Please correct me if I am wrong.

Let us assume that t is the time at which Robin Starts.
Let d be the total distance.
Since we don't know the exact time at which Robin Started, we will have to find out the starting time t.
We will consider all the time in 24 hours time, so that we can calculate the time taken in hours by Robin to reach the office by calculating the difference between the time Robin reaches the office and time when she starts(t) and equating it in the speed-time-distance- formula.

so in 24 hours time zone, 3:00 pm => 15:00

Now we will have to use the speed-time-distance-formula
Distance = Speed * Time
substituting the values,
$$d=(15-t)*20$$ .....(i) => this is the case when Robin travels at a speed of 20km/h and reaches office at 3pm(15:00 in 24 hours time zone)
$$d=(11-t)*30$$ .....(ii) => this is the case when Robin travels at a speed of 30km/h and reaches office at 11 am(11:00 in 24 hours time zone)

From equations (i) and (ii), we get,
$$20*(15-t)=30*(11-t)\\ 300-20t=330-30t\\ 10t=30\\ t=3\\$$
$$d = (11-3)*30=240$$

Now let s be the speed at which Robin has to travel to reach office at 1:00 pm(13:00 24 hours).

We will again use the speed-time-distance-formula,

$$d = s*t$$

on substituting the values, we get,
$$240=s*(13-3)\\ 240=s*10\\ s=24$$

so option B, 24km/h is the correct answer.
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Re: If Robin drives at 20 kilometer per hour, she reaches office at 3 pm. [#permalink]
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Bunuel wrote:
If Robin drives at 20 kilometer per hour, she reaches office at 3 pm. If she drives at 30 kilometer per hour, she reaches office at 11 am. At what speed she should drive if she wishes to reach office at 1 pm ?

A. 23 kilometer per hour
B. 24 kilometer per hour
C. 25 kilometer per hour
D. 26 kilometer per hour
E. 27 kilometer per hour

Use Ratios:

Ratio of speeds = 20:30
Ratio of time taken = 3:2 (inversely proportional)
The difference of 1 in time taken is actually equal to 4 hrs (3pm - 11 am). So actual time taken in the two cases is 12 hrs and 8 hrs.

If time taken needs to be 10 hrs, ratio of time taken = 12:10 = 6:5 (in case of 20km/hr and New case)
Ratio of speeds = 5 : 6 = 20 : S
S = 24 km/hr

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Re: If Robin drives at 20 kilometer per hour, she reaches office at 3 pm. [#permalink]
Let the distance = x km

x/20 – x/30 = 4(Distance/ Rate = Time and Difference between 11 am and 3 pm is equal to 4 hours)

3x – 2x/60 = 4
x/60 = 4
x = 240

When he reaches at 3 pm, he will take time = 240/20 = 12 hours

If he wants to reach
Now , rate * time = Distance
R = 240/10(As he wants to reach at 1 pm, he will take 10 hours)
R = 24 km/hour

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Re: If Robin drives at 20 kilometer per hour, she reaches office at 3 pm. [#permalink]
Bunuel wrote:
If Robin drives at 20 kilometer per hour, she reaches office at 3 pm. If she drives at 30 kilometer per hour, she reaches office at 11 am. At what speed she should drive if she wishes to reach office at 1 pm ?

A. 23 kilometer per hour
B. 24 kilometer per hour
C. 25 kilometer per hour
D. 26 kilometer per hour
E. 27 kilometer per hour

Let t = the number of hours she should drive in order to reach her office at 1 pm. We can create the equation:

20(t + 2) = 30(t - 2)

20t + 40 = 30t - 60

100 = 10t

10 = t

Thus, the distance is 20 x 12 = 240 (or 30 x 8 = 240) km.

So, if Robin wants to arrive at 1 pm, she should drive at 240/10 = 24 kmph.

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Re: If Robin drives at 20 kilometer per hour, she reaches office at 3 pm. [#permalink]
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Re: If Robin drives at 20 kilometer per hour, she reaches office at 3 pm. [#permalink]
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