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If Car A took n hours to travel 2 miles and Car B took m hou
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09 Jul 2020, 11:26
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. \(\frac{10nm}{3n + 2m}\)
B. \(\frac{3n + 2m}{10(n + m)}\)
C. \(\frac{2n + 3m}{5nm}\)
D. \(\frac{10(n + m)}{2n + 3m}\)
E. \(\frac{5(n + m)}{2n + 3m}\)
A. \(\frac{10nm}{3n + 2m}\)
B. \(\frac{3n + 2m}{10(n + m)}\)
C. \(\frac{2n + 3m}{5nm}\)
D. \(\frac{10(n + m)}{2n + 3m}\)
E. \(\frac{5(n + m)}{2n + 3m}\)
Re: If Car A took n hours to travel 2 miles and Car B took m hou
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09 Jul 2020, 18:11
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
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
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10 Jul 2020, 07:31
10 Jul 2020, 07:31
1
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. \(\frac{10nm}{3n + 2m}\)
B. \(\frac{3n + 2m}{10(n + m)}\)
C. \(\frac{2n + 3m}{5nm}\)
D. \(\frac{10(n + m)}{2n + 3m}\)
E. \(\frac{5(n + m)}{2n + 3m}\)
A. \(\frac{10nm}{3n + 2m}\)
B. \(\frac{3n + 2m}{10(n + m)}\)
C. \(\frac{2n + 3m}{5nm}\)
D. \(\frac{10(n + m)}{2n + 3m}\)
E. \(\frac{5(n + m)}{2n + 3m}\)
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
