Ramesh leaves home at 5pm to pick up his daughter from school and returns home at 7 pm. One day the school was over at 5pm and the daughter instead of waiting for her father started walking towards home. Ramesh as usual started from home and met his daughter on the way and returned home 12 minutes earlier. If speed of Ramesh's car is 40km/hr, find the speed in km/hr of his daughter
a 40/9
b 29/8
c 39/7
d 35/8
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Distance speed n time
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romitvsingh
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Mike@Magoosh
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Hi, there. I'm happy to give my two cents on this one. 
This is a cool question! Here's my analysis:
Ramesh leaves home at 5pm to pick up his daughter from school and returns home at 7 pm
So, the trip there takes an hour, and the trip home takes an hours.
The speed of Ramesh's car is 40km/hr
So, the school is 40 km away from home.
One day the school was over at 5pm and the daughter instead of waiting for her father started walking towards home. Ramesh as usual started from home and met his daughter on the way and returned home 12 minutes earlier.
So, instead of turning around at the school, Ramesh drove to some intermediate distance, where he met his daughter, and drove home from that place. Obviously, the trip to that place and from that place must have taken the same time, so he got to that place 6 minutes before 6 pm, in 54 minutes, and drove home from there in 54 minutes. 54/60 = 9/10 hour.
Therefore the distance to that place is:
D = RT = (40 km/hr)*(9/10 hr) = 36 km
The point where Ramesh met his daughter is 36 km away from home. This means, the daughter walked 4 km in that time.
The daughter walked 4 km in 9/10 hour. So
R = D/T = (4)/[9/10] = 40/9 km/hr
Answer = A
Great question. Here's another practice question on speed:
https://gmat.magoosh.com/questions/5
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Let me know if you have any further questions.
Mike
This is a cool question! Here's my analysis:
Ramesh leaves home at 5pm to pick up his daughter from school and returns home at 7 pm
So, the trip there takes an hour, and the trip home takes an hours.
The speed of Ramesh's car is 40km/hr
So, the school is 40 km away from home.
One day the school was over at 5pm and the daughter instead of waiting for her father started walking towards home. Ramesh as usual started from home and met his daughter on the way and returned home 12 minutes earlier.
So, instead of turning around at the school, Ramesh drove to some intermediate distance, where he met his daughter, and drove home from that place. Obviously, the trip to that place and from that place must have taken the same time, so he got to that place 6 minutes before 6 pm, in 54 minutes, and drove home from there in 54 minutes. 54/60 = 9/10 hour.
Therefore the distance to that place is:
D = RT = (40 km/hr)*(9/10 hr) = 36 km
The point where Ramesh met his daughter is 36 km away from home. This means, the daughter walked 4 km in that time.
The daughter walked 4 km in 9/10 hour. So
R = D/T = (4)/[9/10] = 40/9 km/hr
Answer = A
Great question. Here's another practice question on speed:
https://gmat.magoosh.com/questions/5
When you submit your answer to this question, the next page will have the video explanation. At Magoosh, each of our 800+ GMAT practice questions have an accompanying video explanation. We are having a sale right now, ending later this week, so you will never find GMAT prep of this quality so cheap. It's an excellent time to check out Magoosh.
Let me know if you have any further questions.
Mike
Magoosh GMAT Instructor
https://gmat.magoosh.com/
https://gmat.magoosh.com/
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ronnie1985
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This problem can be solved using the relative velocity concept of Physics, which is mush easier to understand and apply. In the onward journey, total distance is 40 km (easily calculable) and the relative velocity is 40+x, where x is the velocity of the daughter. They meet at time 40/(40+x) hours. In this time the daughter has moved distance = x*40/(40+x). In the reverse journey the velocity is that of the father = 40 kmph. and distance = 40-40*x/(40+x). Therefore, 40/ (40+x) + [40-40*x/(40+x)]/[40] = 2-12/60
which on solving gives x = 40/9 kmph.
which on solving gives x = 40/9 kmph.
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Got this question in say some time, but finally got it. This question does not seem to be a 700 level question, but atleast a 650 one.
And also this is a bit difficult to explain or give a solution, at least I found it difficult to explain...
I will say that the answer is A. Interesting question...
And also this is a bit difficult to explain or give a solution, at least I found it difficult to explain...
I will say that the answer is A. Interesting question...
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I think I will try to explain:
Overall Distance it takes in usual for Ramesh to travel is 2 hrs. i.e 120/60.
Total distance travelled is 80 kms.
We know that on that particular day the time taken was less by 12 mins. SO the distance travelled must be lesser accordingly.
Now compare, 80kms 120/60
x 12/60
In this case you get x (or the distance not traveled by Ramesh as his daughter had already started walking) you get x as 8kms.
Remember that 8kms is total, so one way or Ramesh found his daughter 4kms before his usual route.
Now Ramesh's daughter walked 4 kms. as the total distance.
And Ramesh with a speed of 40km/hr covered a distance of 36 km on that day (as his daughter started walking earlier).
So the time taken by the daughter = the time taken by Ramesh to travel 4 km less than the usual i.e 36 km.
SO time = Distance/speed = 36/40 = 9/10
SO his daughter's speed = Distance/time = 4/9/10 = 40/9
This is the speed of Ramesh's Daughter to travel those 4 kms...
Hope this helps for you to understand...
Overall Distance it takes in usual for Ramesh to travel is 2 hrs. i.e 120/60.
Total distance travelled is 80 kms.
We know that on that particular day the time taken was less by 12 mins. SO the distance travelled must be lesser accordingly.
Now compare, 80kms 120/60
x 12/60
In this case you get x (or the distance not traveled by Ramesh as his daughter had already started walking) you get x as 8kms.
Remember that 8kms is total, so one way or Ramesh found his daughter 4kms before his usual route.
Now Ramesh's daughter walked 4 kms. as the total distance.
And Ramesh with a speed of 40km/hr covered a distance of 36 km on that day (as his daughter started walking earlier).
So the time taken by the daughter = the time taken by Ramesh to travel 4 km less than the usual i.e 36 km.
SO time = Distance/speed = 36/40 = 9/10
SO his daughter's speed = Distance/time = 4/9/10 = 40/9
This is the speed of Ramesh's Daughter to travel those 4 kms...
Hope this helps for you to understand...
IT IS TIME TO BEAT THE GMAT
LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!
Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.
LEARNING, APPLICATION AND TIMING IS THE FACT OF GMAT AND LIFE AS WELL... KEEP PLAYING!!!
Whenever you feel that my post really helped you to learn something new, please press on the 'THANK' button.
