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e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2911
While making a non-stop trip, a bus averaged m mph for the first 5  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 57% (02:01) correct 43% (02:03) wrong based on 116 sessions

HideShow timer Statistics While making a non-stop trip, a bus averaged m mph for the first 5 hours and n mph, for the remaining 4 hours. What was the average speed of the bus, in mph, for the whole trip?

Stamement 1: 7.5m + 6n = 465
Statement 2: 2m + 3n = 180

_________________

Originally posted by EgmatQuantExpert on 30 Jul 2018, 21:57.
Last edited by EgmatQuantExpert on 11 Aug 2018, 12:41, edited 1 time in total.
Math Expert V
Joined: 02 Aug 2009
Posts: 7765
Re: While making a non-stop trip, a bus averaged m mph for the first 5  [#permalink]

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While making a non-stop trip, a bus averaged m mph for the first 5 hours and n mph, for the remaining 4 hours. What was the average speed of the bus, in mph, for the whole trip?

Average = $$\frac{5m+4n}{5+4}=\frac{5m+4n}{9}$$
since in statement I we can see a 5m + 4n, work on it

Statement 1: 7.5m + 6n = 465
$$7.5m + 6n = 465$$
multiply the equation by 2..
$$15m+12n=465*2..............3(5m+4n)=3*310..........5m+4n=310$$.
$$\frac{5m+4n}{9}=\frac{310}{9}$$
this is what we are looking for
suff

Statement 2: 2m + 3n = 180
two variables..
insuff
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e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2911
While making a non-stop trip, a bus averaged m mph for the first 5  [#permalink]

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Solution

Given:
• While making a non-stop trip, a bus averaged m mph for the first 5 hours and n mph, for the remaining 4 hours.

To find:
• The average speed of the bus, in mph, for the whole trip.

Approach and Working:
We know, average speed of a journey is equal to the ratio of total distance covered and total time taken to cover that distance.

In this case,
• Total distance covered = 5 x m + 4 x n = 5m + 4n
• Total journey time = 5 + 4 = 9 hours
• Hence, average speed should be $$\frac{5m+4n}{9}$$
So, we can answer the question, if we can find the value of (5m+4n)

Analysing Statement 1
As per the information given in statement 1, 7.5m + 6n = 465
Dividing both sides of the equation by 1.5, we get,
• $$\frac{1}{1.5} (7.5m + 6n) =\frac{1}{1.5} * 465$$
Or, 5m + 4n = 310

As we can find the value of 5m + 4n, we can get our answer.

Hence, statement 1 is sufficient.

Analysing Statement 2
As per the information given in statement 2, 2m + 3n = 180
From this equation, we cannot separately calculate m and n. Also, we cannot obtain the value of 5m + 4n.

Hence, statement 2 is not sufficient.

Therefore, the correct answer is option A.

_________________ While making a non-stop trip, a bus averaged m mph for the first 5   [#permalink] 10 Aug 2018, 06:36
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