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While making a non-stop trip, a bus averaged m mph for the first 5

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While making a non-stop trip, a bus averaged m mph for the first 5  [#permalink]

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New post Updated on: 11 Aug 2018, 12:41
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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?

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


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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.
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Re: While making a non-stop trip, a bus averaged m mph for the first 5  [#permalink]

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New post 30 Jul 2018, 23:22
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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While making a non-stop trip, a bus averaged m mph for the first 5  [#permalink]

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New post 10 Aug 2018, 06:36

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.

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