Rhonda runs at an average speed of 12 kilometers per hour,

Question

Rhonda runs at an average speed of 12 kilometers per hour, and she bicycles at an average speed of 30 kilometers per hour. When she bicycles to work, her travel time is 2.25 minutes less than when she runs to work. The distance to work, in kilometers, is

A) 27/40
B) 3/4
C) 7/8
D) 11/12
E) 6/5

*kudos for all correct solutions

A) 27/40
B) 3/4
C) 7/8
D) 11/12
E) 6/5

rohit8865 · Accepted Answer

Let distance be x then

x/12 = x/30+2.25/60
solving 
x=3/4 km

Ans B

BrentGMATPrepNow · Answer

When Rhonda bicycles to work, her travel time is 2.25 minutes less than when she runs to work  
It might be useful to start with a "Word Equation"
( Rhonda's running time in hours ) = ( Rhonda's cycling time in hours ) + 2.25/60
 Aside: 2.25 minutes = 2.25/60 hours

travel time = distance/speed 
We know the running and cycling speeds, but we don't know the distance. 
So, let d = distance to work

So, we get:  d/12  =  d/30  + 2.25/60
To eliminate the fractions, multiply both sides by 60 (the LCM of 12, 30 and 60)
We get: 5d = 2d + 2.25
Subtract 2d from both sides: 3d = 2.25
Solve: d = 2.25/3 
Check answer choices . . . not there.

Looks like we need to rewrite 2.25/3 as an equivalent fraction. 
If we take 2.25/3, and multiply top and bottom by 4 we get: 9/12, which is the same as 3/4

Answer: B

RELATED VIDEO 
 https://www.youtube.com/watch?v=nwYjckkMnBE

BillyZ · Answer

Average speed (run) =   12 \frac{km}{hr}

Average speed (bicycle) =   30 \frac{km}{hr}

BillyZ · Answer

Average speed (run) =  12 \frac{km}{hr}

Average speed (bicycle) =  30 \frac{km}{hr}

Distance = Speed*Time

Average Time =  \frac{Average Distance}{{Average Speed}}

Time (Bicycle) = Time (Run) - 2.25 min

*(\frac{60min}{1hr})  = *(\frac{60min}{hr}) - 2.25min

2*distance = 5*distance - 2.25

3*distance = 2.25

distance = \frac{3}{4}

KARTAB · Answer

Let x minutes takes to reach office while running

So (x -2.25) minutes by bicycle to reach office

Distance by run = Distance by bicycle

x*12 = 30*(x - 2.25)

Solve it. x = 15/4 minutes i.e 1/16 hours

Distance = 12 *x or 30*x - 2.25) = 12 * 1/16 = 3/4

gracie · Answer

let t=running time
12/30=(t-3/80)/t
t=1/16 hr
1/16 hr*12 kph=3/4 k distance
B

ScottTargetTestPrep · Answer

We are given that Rhonda runs at an average speed of 12 kilometers per hour and bicycles at an average speed of 30 kilometers per hour. We are also given that when she bicycles to work, her travel time is 2.25 minutes less than when she runs to work.

Since she runs and bicycles the same distance, we can let her distance from home to work = d.

Since time = distance/rate, her time running to work is d/12 and her time bicycling to work is d/30. We also need to convert 2.25 minutes to hours.

2.25 minutes = 2.25/60 = 9/240 = 3/80 hour

We can create the following equation and determine d:

d/12 = 3/80 + d/30

Multiplying the entire equation by 240, we have:

20d = 9 + 8d

12d = 9

d = 9/12 = 3/4

Answer: B

dave13 · Answer

When Rhonda bicycles to work, her travel time is 2.25 minutes less than when she runs to work It might be useful to start with a "Word Equation" ( Rhonda's running time in hours ) = ( Rhonda's cycling time in hours ) + 2.25/60 Aside: 2.25 minutes = 2.25/60 hours Hi GMATPrepNow Why do you divide 2.25 by 60 ? what is the point? And why by 60 ? where from did you get 60? thank you

rahul16singh28 · Answer

Let  d  be the distance.

\frac{d}{12} - \frac{d}{30} = \frac{2.25}{60}

d = 0.75

BrentGMATPrepNow · Answer

Time in hours = (time in minutes)/60

For example, 30 minutes = 30/60 hours = 1/2 hour
And 45 minutes = 45/60 hours = 3/4 hour
And 10 minutes = 10/60 hours = 1/6 hour

So, 2.25 minutes = 2.25/60 hours

sviral90 · Answer

You are the only one who has tried solving it via equating distance and not the time. However, how do you get to 15/4? Shouldn't you be dividing 2.25 minutes by 60 to convert into hours or shouldn't you be converting speed per hour into speed per minute?

Aamirso · Answer

Let the distance be X

X/12 - X/30 = 2.25/60.

Solving for X, we get X = 0.75

B.

Fdambro294 · Answer

Given a constant Distance, speed is directly proportional to Time traveled.

If speed increases by (n / d)

Then Time traveled will DECREASE by n / (d + n)

Her speed increases by: (30 - 12) / 12 = 3/2

This Increase in Speed by 3/2 = n/d

Corresponds to a DECREASE in Time traveled by: 3 / (2 + 3) = 3/5

This decrease in time traveled of 2.25 min (Base Time T) ———> corresponds to a (3/5) Decrease in the Base Time T

9/4 min = (3/5) * T

T = 15/4 minutes ———> this is the time it takes her to travel the distance at Original Speed of 12 kmph

D = S * T ——-remember to convert the Units of minutes into hours

(12 kmph) * (15/4) * (1/60) =

Now it becomes easier to cancel NUM and DEN values

3/4 of a kilometer

Posted from my mobile device

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Rhonda runs at an average speed of 12 kilometers per hour,

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