David drove to work at an average (arithmetic mean) speed of 45 miles

Question

David drove to work at an average (arithmetic mean) speed of 45 miles per hour. After work, David drove home at an average speed of 60 miles per hour. If David spent a total of 2 hours commuting to and from work, how many miles does David drive to work?

A. 48
B. 256/5
C. 360/7
D. 105/2
E. 160/3

SHORTEST METHOD: as per given information
(d/45)+(d/60)= 2
d*(4+3)/180 = 2
d = 360/7

A. 48
B. 256/5
C. 360/7
D. 105/2
E. 160/3

dollytaneja51 · Accepted Answer

Time = Distance / Speed
Assuming distance be x
x/45 + x/60 = 2 hours
7x/180 = 2
x = 360/7
C is the answer

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PKN · Answer

Note:- Travelling distance(To & Fro journeys) is equal.
Distance travelled from home to work=Distance travelled from work to home.
Given,  V_{hw}=45mph ,  V_{wh}=60mph , and total travel time,T=2 hrs

Average speed(h-w-h)=Total distance/Total Time

Or, Total distance(h-w-h)= v_{avg}*T=\frac{2*V_{hw}*V_{wh}}{V_{hw}+V_{wh}}*T  = \frac{2*45*60*2}{45+60} = \frac{720}{7} 
Or, 2*distance from home to work= \frac{720}{7} 
Or, distance from home to work= \frac{360}{7}

Ans. (C)

pushpitkc · Answer

Formula used: Average speed =  \frac{2*a*b}{a + b}  where a,b are the average speeds of the to and fro trips
 
Since David travels one half of the distance at 45 miles per hour and the other half at 60 miles per hour, substituting
the values in the formula, we can calculate the average speed for the entire trip =  \frac{2*45*60}{105} = \frac{360}{7}

David travels a total of 2 hours commuting to and from work.

The total distance that David travels is  \frac{2*360}{7} = \frac{720}{7}  (Distance = Speed*Time)

Therefore, David travels one half of that distance to work, which is  \frac{1}{2}*\frac{720}{7} = \frac{360}{7} miles.  (Option C)

pandeyashwin · Answer

45t = 60(2-t)
t = 120/105 = 8/7
d = 45 * 8/7 = 360/7

jalice · Answer

David travelled from home to work at an speed= 45 mph
David travelled from work to home at an speed= 60 mph
Total time taken for the trip to and fro = 2 hours

Let the time taken from home to work be "t" hrs.
Then time taken from work to home will be "2-t" hrs.
As the distance on both side are equal:
45t=60(2-t)
45t=120-60t
t= 120/105 hrs

Distance= speed*time= 45*120/105= 360/7 miles.

Ans(C)

ScottTargetTestPrep · Answer

We can let the distance each way = d and create the equation for time:

d/45 + d/60 = 2

Multiplying by 180, we have:

4d + 3d = 360

7d = 360

d = 360/7

Answer: C

BrentGMATPrepNow · Answer

Let's start with a " word equation "
We can write: ( David's travel time TO work ) + ( David's travel time FROM work ) = 2 hours
 time = distance/speed

Let d = the distance each way

We can write:  d/45  +  d/60  = 2 
To eliminate the fractions, multiply both sides by 180, the LCM of 45 and 60

We get: 4d + 3d = 360 
Simplify: 7d = 360 
Solve: d = 360/7

Answer: C

Cheers, 
Brent

Sr1994 · Answer

If we take the 2 hours into consideration, the calculation might become a bit long.

If the distance is constant and you are given 2 speed. To find the distance, we can use the below-mentioned formula.

d = (2*S1*S2)/(S1+S2)

Here, S1 = 45
S2 = 60

d= (2*45*60)/(45+60)
=(2*45*60)/(105)

by cancelling common values, we get  D=360/7

Answer C

Akp880 · Answer

David drove to work at an average (arithmetic mean) speed of 45 miles per hour. After work, David drove home at an average speed of 60 miles per hour. If David spent a total of 2 hours commuting to and from work, how many miles does David drive to work?

A. 48
B. 256/5
C. 360/7
D. 105/2
E. 160/3

SHORTEST METHOD: as per given information
(d/45)+(d/60)= 2
d*(4+3)/180 = 2
d = 360/7

A. 48
B. 256/5
C. 360/7
D. 105/2
E. 160/3

SHORTEST METHOD : as per given information
(d/45)+(d/60)= 2
d*(4+3)/180 = 2
 d = 360/7

VERBAL1 · Answer

pandeyashwin

Need help here :

45t = 60(2-t)
t = 120/105 = 8/7
d = 45 * 8/7 = 360/7

Why can't we substitute (2-t) on the other side: ie with 45(t-2)

GmatPoint · Answer

Let the distance from home to the office be x miles.
Thus, While going to the office, time taken = x/45 hours
Also, while returning, time taken = x/60 hours

Given, total time = 2 hours
Thus, 2 = x/45 + x/60
 2 = (4x + 3x)/180
 7x = 360
Thus, x = 360/7.

Thus, the correct option is C.

BVRS · Answer

An alternative to solving this problem from the given methods above:

We know the  distance from home-to-work  =  the distance from work-to-home .

Therefore:

Let  t = time taken to travel to work 
Let  2-t = time taken to travel from work to home  
(This is because the total time is 2 hours)

Therefore:

Rate * Time = Distance 
Because the two distances are equal:
 45mph * t  = 65mph * (2-t)
45t=60(2-t) --> t = 8/7 (simplified)
Therefore distance is   45*t   = 45*(8/7). --> 360/7

Hope it helps.

David drove to work at an average (arithmetic mean) speed of 45 miles

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David drove to work at an average (arithmetic mean) speed of 45 miles

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