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# M03-36

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question is about to find "how far apart will they be exactly 1.5 hours before they meet?". They meet in 4hours[T=360/(25+65)]. So 1.5 hours before they meet means how much they travel in 2.5 hours, Fanny traveled [25*2.5=125/2] and Alexander traveled [65*2.5=325/2], now we can subtract the distance [325/2-125/2]=100. I think they are 100 miles apart.

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nitinagg29 wrote:
question is about to find "how far apart will they be exactly 1.5 hours before they meet?". They meet in 4hours[T=360/(25+65)]. So 1.5 hours before they meet means how much they travel in 2.5 hours, Fanny traveled [25*2.5=125/2] and Alexander traveled [65*2.5=325/2], now we can subtract the distance [325/2-125/2]=100. I think they are 100 miles apart.

Your solution is unnecessarily long and incorrect.

Why are you subtracting distances covered? You should add them to get the distance they covered in 2.5 hours and subtract that from the initial distance:

360 - (325/2 + 125/2) = 135.
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I think this is a high-quality question and I agree with explanation.
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Imagine Fanny and Alexander already met and are standing together, so in order to find distance 1.5 hr before meeting is same as calculating distance of them going away from each other for 1.5 hrs
So the distance is $$1.5*(65+25)$$=135
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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I think this is a high-quality question and I agree with explanation.
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Bunuel wrote:
Official Solution:

Fanny and Alexander are 360 miles apart and are both traveling towards each other in a straight line. Fanny is traveling at a constant rate of 25 miles per hour, while Alexander is traveling at a constant rate of 65 miles per hour. How far apart will they be exactly 1.5 hours before they meet?

A. 135 miles
B. 90 miles
C. 70 miles
D. 65 miles
E. 25 miles

Let's keep it simple! The question asks how far apart Fanny and Alexander will be exactly 1.5 hours before they meet. Since their combined speed is 25 + 65 = 90 miles per hour, 1.5 hours prior to their meeting, they will be 90*1.5 = 135 miles apart.

Hi Bunuel

Hi Bunuel Thank you for the solution.Could you please help me understand the concept applied in this solution? Why did we add up the speeds and then multiplied the result with 1.5 hrs, which are the hrs. spent before they meet.

Thank youBunuel
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Tanisha2819 wrote:
Bunuel wrote:
Official Solution:

Fanny and Alexander are 360 miles apart and are both traveling towards each other in a straight line. Fanny is traveling at a constant rate of 25 miles per hour, while Alexander is traveling at a constant rate of 65 miles per hour. How far apart will they be exactly 1.5 hours before they meet?

A. 135 miles
B. 90 miles
C. 70 miles
D. 65 miles
E. 25 miles

Let's keep it simple! The question asks how far apart Fanny and Alexander will be exactly 1.5 hours before they meet. Since their combined speed is 25 + 65 = 90 miles per hour, 1.5 hours prior to their meeting, they will be 90*1.5 = 135 miles apart.

Hi Bunuel

Hi Bunuel Thank you for the solution.Could you please help me understand the concept applied in this solution? Why did we add up the speeds and then multiplied the result with 1.5 hrs, which are the hrs. spent before they meet.

Thank youBunuel

When two objects move towards each other, you can add their speeds together to find out how quickly they're closing the gap between them. Fanny and Alexander together reduce the distance between them by 90 miles every hour (25 mph for Fanny + 65 mph for Alexander).

So, if you look 1.5 hours before they meet, they'd be 135 miles apart because in that time they would cover that distance at their combined speed. This is why we add their speeds and then multiply by 1.5 hours.
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Bunuel wrote:
Tanisha2819 wrote:
Bunuel wrote:
Official Solution:

Fanny and Alexander are 360 miles apart and are both traveling towards each other in a straight line. Fanny is traveling at a constant rate of 25 miles per hour, while Alexander is traveling at a constant rate of 65 miles per hour. How far apart will they be exactly 1.5 hours before they meet?

A. 135 miles
B. 90 miles
C. 70 miles
D. 65 miles
E. 25 miles

Let's keep it simple! The question asks how far apart Fanny and Alexander will be exactly 1.5 hours before they meet. Since their combined speed is 25 + 65 = 90 miles per hour, 1.5 hours prior to their meeting, they will be 90*1.5 = 135 miles apart.

Hi Bunuel

Hi Bunuel Thank you for the solution.Could you please help me understand the concept applied in this solution? Why did we add up the speeds and then multiplied the result with 1.5 hrs, which are the hrs. spent before they meet.

Thank youBunuel

When two objects move towards each other, you can add their speeds together to find out how quickly they're closing the gap between them. Fanny and Alexander together reduce the distance between them by 90 miles every hour (25 mph for Fanny + 65 mph for Alexander).

So, if you look 1.5 hours before they meet, they'd be 135 miles apart because in that time they would cover that distance at their combined speed. This is why we add their speeds and then multiply by 1.5 hours.

Hello Bunuel Thank you so much with the solution. I solved it using rather long method of finding out in how much time they meet and then subtracting 1.5 hrs from that to get the distance b/w them. Got the wrong answer because of calculation mistake. I do understand the concept of relative speed applied here that we are adding up their speeds because they are moving towards each other.

But why we multiplied their relative speed with 1.5 hrs, I am a little lost here because i thought that we multiply that time with the relative speed in which we want to find out the distance covered by both the people and here we are not doing that, we want to find out how far apart F & A would be from each other 1.5 hrs before they meet. I am not able to grasp the logic behind this. I would be really thankful if you could help me understand this as this method is clearly a time saver and a quicker way to get to the right answer.

Thanks Bunuel
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Tanisha2819 wrote:
Hello Bunuel Thank you so much with the solution. I solved it using rather long method of finding out in how much time they meet and then subtracting 1.5 hrs from that to get the distance b/w them. Got the wrong answer because of calculation mistake. I do understand the concept of relative speed applied here that we are adding up their speeds because they are moving towards each other.

But why we multiplied their relative speed with 1.5 hrs, I am a little lost here because i thought that we multiply that time with the relative speed in which we want to find out the distance covered by both the people and here we are not doing that, we want to find out how far apart F & A would be from each other 1.5 hrs before they meet. I am not able to grasp the logic behind this. I would be really thankful if you could help me understand this as this method is clearly a time saver and a quicker way to get to the right answer.

Thanks Bunuel

I'll try again.

The reason we multiply the relative speed by 1.5 hours is to calculate the distance Fanny and Alexander cover together in that time period before they meet. Since they are moving towards each other, their relative speed is the sum of their individual speeds. By multiplying this combined speed (90 mph) by the time remaining before they meet (1.5 hours), we find out how much distance remains between them at that point. This method gives us the distance between Fanny and Alexander 1.5 hours before they meet.

In other words, 1.5 hours before they meet, the distance between Fanny and Alexander is the distance they would cover together in 1.5 hours. Since they cover that distance at 90 miles per hour, then distance = time × speed = 1.5 × 90 = 135 miles.

Hope it helps.
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I think this is a high-quality question and I don't agree with the explanation. Solution is with respect to 1.5 hours before meeting rather than 1.5 after starting. Although the solution is clashing with explanation but if we change the total distance, the solution will fail
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