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If Car A took n hours to travel 2 miles and Car B took m hou

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If Car A took n hours to travel 2 miles and Car B took m hou [#permalink] New post   09 Jul 2020, 11:26
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If Car A took n hours to travel 2 miles and Car B took m hours to travel 3 miles, which of the following expresses the time it would take Car C, traveling at the average (arithmetic mean) of those rates, to travel 5 miles?


A. 10nm3n+2m

B. 3n+2m10(n+m)

C. 2n+3m5nm

D. 10(n+m)2n+3m

E. 5(n+m)2n+3m
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Farina
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Re: If Car A took n hours to travel 2 miles and Car B took m hou [#permalink] New post   09 Jul 2020, 18:11
1
Answer should be A.

Car A:
time=n hours
distance=2 miles
So rate= dist/time = 2/n

Car B:
time=m hours
distance=3 miles
So rate= dist/time = 3/m

Avg of both rates: (2/n +3/m)/2
Solve it and Rate will be: 2m+3n/2mn

We know rate and distance i.e 2m+3n/2mn and 5 miles

Time= dist/rate
T=5/(2m+3n/2mn)

Solve it and you will get option A as answer
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Re: If Car A took n hours to travel 2 miles and Car B took m hou [#permalink] New post   10 Jul 2020, 07:31
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Carcass wrote:
If Car A took n hours to travel 2 miles and Car B took m hours to travel 3 miles, which of the following expresses the time it would take Car C, traveling at the average (arithmetic mean) of those rates, to travel 5 miles?


A. 10nm3n+2m

B. 3n+2m10(n+m)

C. 2n+3m5nm

D. 10(n+m)2n+3m

E. 5(n+m)2n+3m


If Car A took n hours to travel 2 miles and Car B took m hours to travel 3 miles, which of the following expresses the time it would take Car C, traveling at the average (arithmetic mean) of those rates, to travel 5 miles?

Speed = distance/time
Speed of car A = 2/n
Speed of car B = 3/m

Speed of car C = (2/n + 3/m)/2
= (2m/mn + 3n/mn)/2
= [(2m + 3n)/mn]/(2/1)
= [(2m + 3n)/mn](1/2)
= (2m + 3n)/2mn

Which of the following expresses the time it would take Car C to travel 5 miles?
time = distance/speed
Car C's time = 5/[((2m + 3n)/2mn)]
= 5[2mn/(2m + 3n)]
= 10mn/(2m + 3n)

Answer: A

Cheers,
Brent
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Re: If Car A took n hours to travel 2 miles and Car B took m hou [#permalink]
10 Jul 2020, 07:31
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