VeritasPrepKarishma wrote:
gmihir wrote:
Thanks Bunnel for the great link - awesome questions!!
For this one (two boats heading towards each other) - i calculated the time they would collide with each other (48th min) and then "tried" calculating from there on, taking eons to solve - how can the problem be solved with this apporach ? is 25*1/60 the only way to solve such problems ?
Bunuel has already given you a great and most direct approach for this question. But if you did go the round about way, you could have solved it in this way:
Since their combined speed is 20 + 5 = 25 miles/hr, they cover 20 miles in \(\frac{20}{25}\) hrs i.e. \(\frac{20}{25} * 60\) mins = 48 mins
Now, in 48 mins, they cover 20 miles. So in 1 min, they must have covered 20/48 = 5/12 miles
Responding to a pm:
Quote:
You mentioned in your comment above that "they" cover the distance of 20 miles in 48 minutes. Maybe I am misunderstaning this but how is that possible? The two boats, initially, begin at a distance of 20 miles away from each other, so isn't the 48 minutes the amount of time it will take them to "meet", and not actually cover the whole 20 miles, as you mentioned in your comment above?
Please help me understand as I am still struggling with distances and rate.
The question involves relative speed and in relative speed, we often talk about the combined distance covered by two objects.
Say A and B are standing 20 feet apart. They walk toward each other and now they are 10 feet apart. "They" have covered a distance of 10 feet together. We don't know how much distance which one covered but we know that together they covered 10 feet. Say they took 1 minute to cover the 10 feet together. Then their combined speed is 10 feet per min.
Perhaps A's speed is 4 feet/ min and B's speed is 6 feet /min so that in one minute, they together covered 10 feet.
or perhaps A's speed is 8 feet/ min and B's speed is 2 feet /min so that in one minute, they together covered 10 feet.
or some other such case.
Similarly, when the boats head toward each other, they are together reducing the initial distance between them of 20 miles. When they finally meet, distance between them is 0 miles so they covered 20 miles together. Since they meet each other in 48 mins, it means their combined speed is such that they covered 20 miles in 48 mins.
Does this clarify the situation?
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Karishma
Veritas Prep GMAT Instructor
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