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# How many miles long is the route from Nurich to Greensburg?

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Re: How many miles long is the route from Nurich to Greensburg? [#permalink]
msk0657, in case 2 how can we assume that the speed for the remaining (2d/3) = 'x' mph.
speed was 'x' mph for the remaining 2 hrs of the journey in the 1st case.
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How many miles long is the route from Nurich to Greensburg? [#permalink]
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Find : distance between N and G

Let total distance = D

1) Given Time = 3 hour journey.
Assume speed = x miles/hour for "last" 2 hours . So for "1st" hour speed = x+5 miles /hour

so Distance covered in 1st: 1 hour = x+5
Distance covered in last part: last 2 hours = 2*x =2x

Total distance = D = x+5+2x = 3x+5

No other information. Not sufficient

2) Given : First 1/3rd of journey at 38 miles/ hour
so given for first D/3 distance, speed is 38 miles/ hour

Combining both : 1+2

By 2nd option : Fist 1/3rd of distance has speed 38miles/hour
Means so when Sam started he went by 38 miles/hour for D/3 distance. Or we can say in 1 hour after he started he completed 38 miles.

Now by option 1: In total 3 hour journey... in first 1 hour he completed x+5 miles

Therefore x+5 = 38 => x=33

So Speed for 1st hour = x+5 miles/hour = 38 miles/hour
Speed for remaining 2 hours = x = 33 miles/hour

Total distance covered = 3x+5 = 3*33+5 = 104 miles.

+1 Kudos if you like the solution.

Note : Here catch is "First hour", and "last hour". Generally when we solve such time of question, question confuses us by giving a relation between two variables in 1st option and detail about 1 of the variable in option 2nd. There we don't know which variable is which. But in this question, its explicitly mentioned in option 1 that we are given details about first 1 hour of journey, last 2 hour of journey, total 3 hour journey. And in 2nd option, we get to know speed of "first" 1/3rd of journey. So it all gets adds up.

Originally posted by Nikkb on 31 Aug 2017, 10:37.
Last edited by Nikkb on 04 Sep 2017, 22:51, edited 3 times in total.
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Re: How many miles long is the route from Nurich to Greensburg? [#permalink]
how do we know that 38 miles/ hr is first hour or last hour?
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Re: How many miles long is the route from Nurich to Greensburg? [#permalink]
2
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Tushar2278 wrote:
how do we know that 38 miles/ hr is first hour or last hour?

How many miles long is the route from Nurich to Greensburg?

(1) Sam drove the first hour of the three-hour trip from Nurich to Greensburg at 5 miles per hour faster than he drove the final 2 hours.
(2) Sam drove the first 1/3 of the trip from Nurich to Greensburg at 38 miles per hour.

Tushar2278 : Its mentioned that for "first" 1/3 rd of trip speed is 38miles/hour. So while calculating we check the distance and time from start of journey. Check the answer that i posted. I have tried to explain solution properly.
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How many miles long is the route from Nurich to Greensburg? [#permalink]
Bunuel wrote:
How many miles long is the route from Nurich to Greensburg?

(1) Sam drove the first hour of the three-hour trip from Nurich to Greensburg at 5 miles per hour faster than he drove the final 2 hours.
(2) Sam drove the first 1/3 of the trip from Nurich to Greensburg at 38 miles per hour.

Distance = rate*time

------- (s + 5) ------------- s --------------
--- (first hour) ----(last 2 hours) -------
-------- (D/3) --------(2D/3) -------------

(1) Let s (miles/hr) = speed of last 2 hr = R2
(s + 5) miles/hr = speed of 1st hr = R1
Distance for 1st hr, D1= R1*T1 = (s + 5)(1)
Distance for last 2 hr, D2 = R2*T2 = (s)(2)

Total distance, D = s + 5 + 2s = 3s + 5

(2) 38 miles per hour. So 1 hour, Sam drove 38 miles for (D/3).

(1) + (2) s + 5 = 38 miles/hr, s = 33 miles/hr

D = 3s + 5 = 3(33) + 5 = 99 + 5 = 104 miles
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Re: How many miles long is the route from Nurich to Greensburg? [#permalink]
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Re: How many miles long is the route from Nurich to Greensburg? [#permalink]
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