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# While driving from Corvallis to Portland, Matt obeys the speed limit.

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Re: While driving from Corvallis to Portland, Matt obeys the speed limit. [#permalink]
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Using R*T = D

Matt: 36 * (t + 3/2) = 81
Hence t = 27/36 = 3/4

Now for his friend V:
rate * 3/4 = 81
Hence rate = 81*4/3 = 108
Ans D
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Re: While driving from Corvallis to Portland, Matt obeys the speed limit. [#permalink]
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Given

Matt Speed = 36
Distance = 81
therefore Matt takes 9/4 hours to travell 81 miles

Vadim starts 90 mins late = 3/2 hours
therefore distance travelled bu Vadim in (9/4 - 3/2) hours is?

(9/4-3/2) = 3/4 hours

Distance travelled = 81
minimun time = 3/4

x> 81*(4/3)
x> 108

Therefore D
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Re: While driving from Corvallis to Portland, Matt obeys the speed limit. [#permalink]
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Bunuel wrote:
While driving from Corvallis to Portland, Matt obeys the speed limit. Matt’s friend Vadim likes to drive faster than the speed limit and believes that he could leave well after Matt and still reach Portland first. The distance from Corvallis to Portland is 81 miles and both Matt and Vadim travel the same route at their respective constant speeds. If Matt travels at a constant speed of 36 mph and leaves 90 minutes before Vadim, what is the minimum constant speed that Vadim must exceed in order to arrive in Portland before Matt?

A. 72 mph
B. 81 mph
C. 96 mph
D. 108 mph
E. 162 mph

Kudos for a correct solution.

I too get V's speed to be 108. Since matt travels for 81/36 hours, and V leaves 90 mins or 1.5 hours after him, V travels for (81/36-1.5) hrs. So his speed is
81/(81/36-1.5) which comes to 108.

But here is where I got confused. The questin asked is what is the minimum speed V must "exceed" to arrive... Is this exceed the speed limit (which is matt's speed =36) or just exceed speed x to arrive? If you interpret it as exceed speed limit then answer comes to A = 72mph. If not then 108mph.

Press kudos if I am right.
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Re: While driving from Corvallis to Portland, Matt obeys the speed limit. [#permalink]
Bunuel wrote:
While driving from Corvallis to Portland, Matt obeys the speed limit. Matt’s friend Vadim likes to drive faster than the speed limit and believes that he could leave well after Matt and still reach Portland first. The distance from Corvallis to Portland is 81 miles and both Matt and Vadim travel the same route at their respective constant speeds. If Matt travels at a constant speed of 36 mph and leaves 90 minutes before Vadim, what is the minimum constant speed that Vadim must exceed in order to arrive in Portland before Matt?

A. 72 mph
B. 81 mph
C. 96 mph
D. 108 mph
E. 162 mph

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Solution: D

Start by determining how long it will take Matt to drive from Corvallis to Portland. D = RT, D = 81, and Matt’s R = 36, so 81 = 36T. Isolating T yields T = 81/36, or 9/4, or 2 ¼, or 2 hours and 15 minutes. This means that 90 minutes into the trip, Matt will be 45 minutes (or ¾ of an hour) from Portland. At this point we have a race: in order to beat Matt to Portland, Vadim needs to travel 81 miles in under ¾ of an hour. To find the minimum acceptable speed, return to D = RT. Vadim’s D = 81, his T = ¾, so 81 = R(¾). R = 108 and Vadim must exceed 108mph in order to arrive in Portland first.
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Re: While driving from Corvallis to Portland, Matt obeys the speed limit. [#permalink]
1
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Bunuel wrote:
While driving from Corvallis to Portland, Matt obeys the speed limit. Matt’s friend Vadim likes to drive faster than the speed limit and believes that he could leave well after Matt and still reach Portland first. The distance from Corvallis to Portland is 81 miles and both Matt and Vadim travel the same route at their respective constant speeds. If Matt travels at a constant speed of 36 mph and leaves 90 minutes before Vadim, what is the minimum constant speed that Vadim must exceed in order to arrive in Portland before Matt?

A. 72 mph
B. 81 mph
C. 96 mph
D. 108 mph
E. 162 mph

Kudos for a correct solution.

Speed of Matt = 36 mph

Now Matt Leaves 90 minutes before vadim. So, during this time Matt travels 36*90/60 = 54 Miles
The distance left to reach Portland = 81 - 54 = 27 miles

At this time Vadim starts travelling and he has to travel atleast 81 miles during the time Matt travels next 27 miles
So,
27/81 = 36/v
-> v = 108
So if vadim has a speed just greater than 108 he will reach before matt....

So, vadim must exceed 108 mph in order to arrive in Portland before Matt

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Re: While driving from Corvallis to Portland, Matt obeys the speed limit. [#permalink]
Bunuel wrote:
While driving from Corvallis to Portland, Matt obeys the speed limit. Matt’s friend Vadim likes to drive faster than the speed limit and believes that he could leave well after Matt and still reach Portland first. The distance from Corvallis to Portland is 81 miles and both Matt and Vadim travel the same route at their respective constant speeds. If Matt travels at a constant speed of 36 mph and leaves 90 minutes before Vadim, what is the minimum constant speed that Vadim must exceed in order to arrive in Portland before Matt?

A. 72 mph
B. 81 mph
C. 96 mph
D. 108 mph
E. 162 mph

We are given that Matt travels at a rate of 36 mph and leaves 90 minutes, or 1.5 hours, before Vadim. We can let Vadim’s time = t, so Matt’s time = t + 1.5. Since rate x time = distance, we can create the following equation and solve for t:

36(t + 1.5) = 81

36t + 54 = 81

36t = 27

t = 27/36 = ¾

So, we know Vadim must reach Portland in ¾ of an hour or less. Since rate = distance/time, his minimum speed is 81/(¾) = 81 x 4/3 = 108 mph.

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Re: While driving from Corvallis to Portland, Matt obeys the speed limit. [#permalink]
The speed that Vadim must exceed is the speed that would allow him to arrive at Portland in the same time as Matt.

Matt has to travel a distance of 81 miles at a constant speed of 36 mph, which he will be able to do in t= 81/36= 2hours 15 minutes.

Vadim who is 90 minutes late to start his trip, has got: 2hr15min - 90min= 45minutes to catch up with Matt.

The distance he needs to catch up is 36mph x 1,5hrs= 54 miles at a relative speed of (V-36) mph (V is Vadim's speed). We subtract the speeds because they are traveling in the same direction.

Now Vadim has got 45 minutes (3/4hrs) to close a gap of 54 miles at a relative speed of (V-32)mph.
Setting this as an equation, we get: (V-36) x 3/4= 54.
Solving for V, we get V= 108mph.

If Vadim travels at a speed of 108 mph, he will be able to catch up with Matt and reach same time as him to Portland. He therefore needs to travel at more than 108mph to arrive at Portland before Matt.

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Re: While driving from Corvallis to Portland, Matt obeys the speed limit. [#permalink]
This question can also be solved using ratios:

Once Valdim will get moving, He and Matt will be traveling for the same period of time.

If the time is same, the ratio of speeds to the ratio of distances must vary directly: M (speed of Matt)/V(speed of Valdim)= DM (distance of Matt)/DV (distance of Valdim)= (81-54)/81= 27/81=1/3.

Therefore, the ratio of speed of Matt to the speed of Valdim is:
M:V
1:3
The actual speed of Matt is 36 mph, hence the actual speed of Valdim must be 3x36= 108 mph.