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?

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)*[(d/5)+(d/7)]= 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.

[quote="skylimit"]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.

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)

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

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.

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.
_________________

Consistency is the Key

Thanks