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Jasmin and Ron drive at constant speeds toward each other on a certain

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Jasmin and Ron drive at constant speeds toward each other on a certain  [#permalink]

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New post 24 May 2015, 03:35
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Question Stats:

66% (02:30) correct 34% (02:39) wrong based on 200 sessions

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Jasmin and Ron drive at constant speeds toward each other on a certain route. Jasmin drives at a constant speed of 25 miles per hour. At a certain time they pass by each other, and then keep on driving away from each other, maintaining their speeds. If Jasmin is 105 miles away from Ron at 8am, and also 105 miles away from Ron later, at 11am, then Ron is driving at how many miles per hour?

A. 10
B. 15
C. 20
D. 35
E. 45

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Re: Jasmin and Ron drive at constant speeds toward each other on a certain  [#permalink]

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New post 24 May 2015, 07:09
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In the 3 hours between 8am and 11am, the two of them combined covered a total of 105+105 = 210 miles. So together, they're covering 210/3 = 70 miles per hour. That must be the sum of their speeds, so if Jasmin is driving 25 miles per hour, then Ron's speed is 70-25 = 45 mph.
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Jasmin and Ron drive at constant speeds toward each other on a certain  [#permalink]

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New post 21 Jun 2015, 03:31
I cannot say that I understand the question... I ended up with 25.

First of all, we don't know at what time they start travelling. Saying that at 8.00 they are 105 miles apart and at 11.00 they are 105 miles apart as well, only tells us that this is how many km apart from each other they were at these 2 times.

So, what I did was to start at a distance of 105 km difference:

Time..............J....R
8.00............105....0
9.00............130
10.00..........155
11.00..........180....75

Now, at 11.00 they are 180-105 = 75 km apart.
It has been 3 hours and R covered 75 km.
So, 75/3 = 25.

I don't see how we can assume that 105+105 = 210 km is the total distance they have covered...
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Re: Jasmin and Ron drive at constant speeds toward each other on a certain  [#permalink]

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New post 21 Jun 2015, 03:40
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pacifist85 wrote:
I cannot say that I understand the question... I ended up with 25.

First of all, we don't know at what time they start travelling. Saying that at 8.00 they are 105 miles apart and at 11.00 they are 105 miles apart as well, only tells us that this is how many km apart from each other they were at these 2 times.

So, what I did was to start at a distance of 105 km difference:

Time..............J....R
8.00............105....0
9.00............130
10.00..........155
11.00..........180....75

Now, at 11.00 they are 180-105 = 75 km apart.
It has been 3 hours and R covered 75 km.
So, 75/3 = 25.

I don't see how we can assume that 105+105 = 210 km is the total distance they have covered...


Hi,
J and R are 105 kms away and are travelling towards each other. they meet each other after sometime, which means they travelled this 105 kms and they continue travelling . now they are moving away from each other and at 11 are 105 kms away from each other...
so they have travelled 105 kms + 105 kms= 210 kms...
they start at 8 and have travelled 210 kms at 11. so total time =3 hrs ..
their combined speed =210/3=70kms.
J ha s25 kph speed so R's speed =70-25=45kph
ans E
hope it is clear
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Re: Jasmin and Ron drive at constant speeds toward each other on a certain  [#permalink]

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New post 21 Jun 2015, 04:12
chetan2u wrote:
pacifist85 wrote:
I cannot say that I understand the question... I ended up with 25.

First of all, we don't know at what time they start travelling. Saying that at 8.00 they are 105 miles apart and at 11.00 they are 105 miles apart as well, only tells us that this is how many km apart from each other they were at these 2 times.

So, what I did was to start at a distance of 105 km difference:

Time..............J....R
8.00............105....0
9.00............130
10.00..........155
11.00..........180....75

Now, at 11.00 they are 180-105 = 75 km apart.
It has been 3 hours and R covered 75 km.
So, 75/3 = 25.

I don't see how we can assume that 105+105 = 210 km is the total distance they have covered...


Hi,
J and R are 105 kms away and are travelling towards each other. they meet each other after sometime, which means they travelled this 105 kms and they continue travelling . now they are moving away from each other and at 11 are 105 kms away from each other...
so they have travelled 105 kms + 105 kms= 210 kms...
they start at 8 and have travelled 210 kms at 11. so total time =3 hrs ..
their combined speed =210/3=70kms.
J ha s25 kph speed so R's speed =70-25=45kph
ans E
hope it is clear


Actually, I realised my mistake... Because they are travelling towards each other, I should have subtracted the distance that was being covered by the one travelling at 25 km, instead of adding it...
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Jasmin and Ron drive at constant speeds toward each other on a certain  [#permalink]

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New post Updated on: 11 May 2018, 09:39
reto wrote:
Jasmin and Ron drive at constant speeds toward each other on a certain route. Jasmin drives at a constant speed of 25 miles per hour. At a certain time they pass by each other, and then keep on driving away from each other, maintaining their speeds. If Jasmin is 105 miles away from Ron at 8am, and also 105 miles away from Ron later, at 11am, then Ron is driving at how many miles per hour?

A. 10
B. 15
C. 20
D. 35
E. 45


let r=Ron's rate
3/2 hrs*(25+r) mph=105 miles
r=45 mph
E

Originally posted by gracie on 09 Jan 2017, 18:34.
Last edited by gracie on 11 May 2018, 09:39, edited 1 time in total.
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Re: Jasmin and Ron drive at constant speeds toward each other on a certain  [#permalink]

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New post 21 Feb 2018, 11:41
J(start)<--------------105------------->R(start) => 8 AM
R(end)<----30----->J(start)-----------75-----------J(end)----30----R(start) => 11AM
so (75 + 30 + 30)/3 = R speed, R = 45 m/hr
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Re: Jasmin and Ron drive at constant speeds toward each other on a certain  [#permalink]

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New post 22 Feb 2018, 00:23
This is a different and slightly more detailed/explanatory approach which, I hope, will alleviate the confusion. Following are the positions of Jasmin (J) and Ron (R) at three different points of time: (A) at 8:00am when they are 105 miles apart and driving towards each other; (B) when they meet after driving for (say) t hours; and (C) at 11:00am when they are again 105 miles apart after driving away from each other.
(A) J>>……………………………………………<<R at 8:00am
(B) ……………..(J/R)…………………….. at (8+t) am
(C) <<R…………………………………………….>>J at 11:00am
Jasmin and Ron each drive continuously for 3 hours (8:00am to 11:00am). Let us break this down into two segments: (i) when they drive towards each other until they meet and (ii) when they drive away from each other until they are again 105 miles apart. Assuming Ron’s speed is x mph, Jasmin and Ron cover 25t and xt miles respectively until they meet (Segment (i)) and 25(3-t) miles and x(3-t) miles when they drive away from each other after crossing and until they are again 105 miles apart (Segment (ii)). But in each of the segments they are covering 105 miles. So we can formulate the following equations:
(i) 25t + xt = 105 >> t=(105/25+x)
(ii) 25(3-t) + x(3-t)=105>> Substituting the value of t from (i) x=45 mph. Answer: E.
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Re: Jasmin and Ron drive at constant speeds toward each other on a certain  [#permalink]

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New post 22 Feb 2018, 01:26
2
reto wrote:
Jasmin and Ron drive at constant speeds toward each other on a certain route. Jasmin drives at a constant speed of 25 miles per hour. At a certain time they pass by each other, and then keep on driving away from each other, maintaining their speeds. If Jasmin is 105 miles away from Ron at 8am, and also 105 miles away from Ron later, at 11am, then Ron is driving at how many miles per hour?

A. 10
B. 15
C. 20
D. 35
E. 45


The distance between them is 105 miles and after 3 hrs it is 105 miles again. So they must have been 105 miles away while they were travelling towards each other and then after they met, they would have traveled another 105 miles away from each other. So they have together traveled 105+105 = 210 miles in 3 hrs.

Relative Speed = 210/3 = 70 = Speed of Jasmin + Speed of Ron (since they were travelling towards each other)
Jasmin drives at 25 mph so Ron drives at 70 - 25 = 45 mph.

Answer (E)
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Re: Jasmin and Ron drive at constant speeds toward each other on a certain  [#permalink]

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New post 26 Feb 2018, 09:45
1
reto wrote:
Jasmin and Ron drive at constant speeds toward each other on a certain route. Jasmin drives at a constant speed of 25 miles per hour. At a certain time they pass by each other, and then keep on driving away from each other, maintaining their speeds. If Jasmin is 105 miles away from Ron at 8am, and also 105 miles away from Ron later, at 11am, then Ron is driving at how many miles per hour?

A. 10
B. 15
C. 20
D. 35
E. 45


We use the formula: rate x time = distance. We know that Jasmin’s distance plus Ron’s distance = 2 x 105 = 210 miles. Letting Ron’s rate = r, we can create the equation:

25(3) + 3r = 210

3r = 135

r = 45

Answer: E
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Re: Jasmin and Ron drive at constant speeds toward each other on a certain &nbs [#permalink] 26 Feb 2018, 09:45
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