Cole drove from home to work at an average speed of 75 kmh. He then

Question

Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
A) 66
B) 70
C) 72
D) 75
E) 78

Round-trip average speed: (2*75*105)/(75+105)=525/6
Round-trip time=2 hrs given
So round-trip distance=(526/6)*2=175 kms
Single-trip distance=175/2 kms...Time taken to cover this distance at 75kmph= (175/2)/75 hrs=70 mins.

zurvy · Accepted Answer

Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
A) 66
B) 70
C) 72
D) 75
E) 78

Hi All,

Here is my first post...

I prefer to use the ratio approach when it is possible, in this case it is.

The ratios between the speeds Work:Home = 75:105 = 5:7
Given that the distance in both directions is the same, the ratios of times becomes Work:Home = 7:5 (inverse)

The total time is given 2 hours ==> , so: 2/12 *7 = 14/12 hours ==> Multiple by 5 to get minutes = 70/60 ==> Answer is 70 minutes.

skylimit · Answer

I tried solving the question by starting with this:
time to work + time home = 2
d/75 + d/105 = 2
105d/7875 + 75d/7875 = 15750
180d/7875 = 15750
180d = 7875*15750
I used my calculator for the rest and got d = 689062.5 which is obviously too big to work with the question. 
So I stopped. 
What went wrong?

sunnysid · Answer

Let the distance one way be x
Time from home to work = x/75
Time from work to home = x/105
Total time = 2 hrs
(x/75) + (x/105)= 2
Solving for x, we get x = 175/2

Time from home to work in minutes= (175/2)*60/75 = 70 minutes

Ans= B

sunnysid · Answer

The error lies in your 2nd step- 105d/7875 + 75d/7875 = 15750

It should be 105d/7875 + 75d/7875 =   2

A better approach would be to take the common factors out. This way the calculation becomes much simpler. In this case taking common factor "15" out we get:

(1/15)* = 2 --> (d/5)+(d/7)=30; which is much easier to solve manually. Remember, if you think you need a calculator on any GMAT question then probably your approach is not correct. There is always a way around.

skylimit · Answer

Shoot! Nice catch. Thanks

skylimit · Answer

The inverse method is interesting and it seems pretty fast too. 
I just don't understand the very last part above. 
Why did you multiply 2/12 by 7 and then multiply by 5 to get minutes?

zurvy · Answer

Hi there,

The ratio of time is as explained 5:7 during the entire trip , and it took a total of 2 hours ==> Imagine it like this, you have to split the 2 hours 
with a ratio of 5:7 ==> The total parts would be in this case 5+7 = 12 ==> so The total time has to be divided first by 12, and then multiplied by 5.
If I told you to split 24 apples among two persons with a ratio of 5:7, you would first divide 24/12 (12=7+5) and than multiple by 5 and 7 respectively to get the answer.
24/12 * 5 = 10 for one person 24/12 * 7 = 14 for the other making a total of 24 apples.

Regarding the multiplication by 5, you need to convert 14/12 to fractions of 60 (so you get the minutes).
(5*14/5*12 = 70/60)
Or you could, 14/12 = 7/6 hour = 1 1/6 hour = 1 hour and 10 minutes = 70/60 hour (its just playing with fractions, and with time, having a denominator of 60, always
gives you the number of minutes at the top)

skylimit · Answer

Thanks zurvy!
I didn't realize you multiplied by 5 to get a denominator of 60. 
Nice solution

gracie · Answer

let t=time to work
time to home (derived from inverse kmh ratio)=75t/105➡5t/7
t+5t/7=2 hours total time
t=7/6 hours➡70 minutes

mbaonly2014 · Answer

Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
A) 66
B) 70
C) 72
D) 75
E) 78

Answer : B

First round distance travelled (say) = d
Speed = 75 k/h
Time taken, T2 = d/75 hr

Second round distance traveled = d (same distance)
Speed = 105 k/h
Time taken, T2 = d/105 hr

Total time taken = 2 hrs
Therefore , 2 = d/75 + d/105
LCM of 75 and 105 = 525

2= d/75 + d/105
=> 2 = 7d/525 + 5d/525
=> d = 525 / 6 Km

Therefore, T1= d/75
=> T1 = 525 / (6 x 75)
=> T1 = (7 x 60) / 6 -- in minutes
=> T1 = 70 minutes.

iqbalfiery · Answer

Cole drove from home to work at an average speed of 75 kmh. He then returned home at an average speed of 105 kmh. If the round trip took a total of 2 hours, how many minutes did it take Cole to drive to work?
A) 66
B) 70
C) 72
D) 75
E) 78

Round-trip average speed: (2*75*105)/(75+105)=525/6
Round-trip time=2 hrs given
So round-trip distance=(526/6)*2=175 kms
Single-trip distance=175/2 kms...Time taken to cover this distance at 75kmph= (175/2)/75 hrs=70 mins.

santro789 · Answer

Time = distance /speed

So Lets consider D =100

Therefore , 100/75(60) +100/105(50)= 120 mins

Is the right way of thinking ?

Can someone please explain this with logic not formulas

laddaboy · Answer

It is incorrect to assume the value of distance D as we have a constrain on time ( t1+t2 = 2 hours ).

We know the avg speed for first half is 75kmph => D = 75 * T1 
We also know the avg speed for second half is 105kmph => D = 105*T2

Since the distance is same we can equate the above equations 75*T1 = 105*T2 => 5T1=7T2.
Now we know the total time taken is 2 hours => T1+T2 = 2
On solving we will get T1 = 7/6 hours which is 70 minutes.

ScottTargetTestPrep · Answer

We use the formula distance = rate x time, or equivalently, time = distance/rate. We can let the distance either way = d; thus, Cole’s time from home to work is d/75 and his time from work to home is d/105. The total travel time is given as 2 hours, so we have:

d/75 + d/105 = 2

Multiplying the entire equation by 525, we have:

7d + 5d = 1050

12d = 1050

d = 1050/12 = 525/6 = 175/2 km

Thus, it took him (175/2)/75 = 175/150 = 7/6 hours = 7/6 x 60 = 70 minutes.

Answer: B

Buttercup3 · Answer

Thanks

generis · Answer

I avoid division if I can in RTD problems. I solved for time with multiplication. It's fast.

Total time = 2 hours

Let time from home to work = x
So time from work to home = (2-x)

Rate, home to work = 75 kmh
Rate, work to home = 105 kmh

r*t=D

D, home to work: (75*x)
D, work to home: (105)*(2-x)

D  is equal both ways, hence

75x = (105)(2-x) 
 75x = 210 - 105x 
 180x = 210

x = \frac{210}{180} = \frac{21}{18} =\frac{7}{6}hrs

Any fraction of an hour can be multiplied by 60 to obtain minutes.

x =\frac{7}{6}hrs * 60  = 70 minutes

Answer B

AkshdeepS · Answer

Speed from home to work = 75 kmph

Say time spent = t hours

Therefore distance travelled = 75t kms

Speed from work to home = 105 kmph

Time spent = (2 - t) hours {as total time is 2 hours)

Distance travelled = 105 (t - 2) = 105t - 210 kms

As both distances are same, we can equate distances:

105t - 210 = 75t

t = 210/180 = 7/6

t = 7/6 * 60

t = 70 minutes

BrentGMATPrepNow · Answer

Let's start with a word equation:   distance traveled going to work  =  distance traveled going home

Let   t   = the Cole's travel time (in hours) going to work
So,   2 - t   = the Cole's travel time going home

Distance = (rate)(time) , so we can plug our values into the word equation to get:   75t  =  105(2 - t)  
Expand the right side:  75t = 210 - 105t 
Add 105t to both sides:  180t = 210  
Solve:  t = 210/180  (hours)
Divide numerator and denominator by 3 to get:  t = 70/60  HOURS

We want the travel time to be expressed in MINUTES. 
 70/60  HOURS = 70 minutes

Answer: B

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