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A car has to travel from New York to Chicago at an average speed of 40
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17 Jun 2025, 00:58
17 Jun 2025, 00:58
Expert Reply
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Question Stats:
75% (01:36) correct
25% (01:55) wrong based on 4 sessions
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A car has to travel from New York to Chicago at an average speed of 40 miles per hour and return immediately along same route at an average speed of 60 miles per hour. What is the average speed, in miles per hour, for the round trip?
(A) 45
(B) 48
(C) 50
(D) 51
(D) 55
(A) 45
(B) 48
(C) 50
(D) 51
(D) 55
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Re: A car has to travel from New York to Chicago at an average speed of 40
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17 Jun 2025, 01:10
17 Jun 2025, 01:10
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avg speed = total distance / total time
=let distance from one side is x so total roundtrip distance is 2x,
time=distance/speed
,
so avg speed=2x/(x/40 + x/60) which will give 48 as answer
=let distance from one side is x so total roundtrip distance is 2x,
time=distance/speed
,
so avg speed=2x/(x/40 + x/60) which will give 48 as answer
Re: A car has to travel from New York to Chicago at an average speed of 40
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19 Jun 2025, 04:00
19 Jun 2025, 04:00
Expert Reply
Let $D$ be the distance from New York to Chicago.
Time to New York to Chicago (Trip 1):
Speed $\left(S_1\right)=40 \mathrm{mph}$
Time $\left(T_1\right)=$ Distance $/$ Speed $=D / 40$ hours
Time to return from Chicago to New York (Trip 2):
Speed $\left(S_2\right)=60 \mathrm{mph}$
Time $\left(T_2\right)=$ Distance $/$ Speed $=D / 60$ hours
Total Distance for the Round Trip:
Total Distance $=$ Distance to Chicago + Distance from Chicago $=D+D=2 D$ miles
Total Time for the Round Trip:
Total Time $=$ Time for Trip $1+$ Time for Trip $2=D / 40+D / 60$ hours
To add the fractions, find a common denominator (which is 120):
$D / 40+D / 60=(3 D / 120)+(2 D / 120)=5 D / 120=D / 24$ hours
Average Speed for the Round Trip:
Average Speed = Total Distance / Total Time
Average Speed $=2 D /(D / 24)$
Average Speed $=2 D \times(24 / D)$
Average Speed $=2 \times 24$
Average Speed $=48$ miles per hour
Time to New York to Chicago (Trip 1):
Speed $\left(S_1\right)=40 \mathrm{mph}$
Time $\left(T_1\right)=$ Distance $/$ Speed $=D / 40$ hours
Time to return from Chicago to New York (Trip 2):
Speed $\left(S_2\right)=60 \mathrm{mph}$
Time $\left(T_2\right)=$ Distance $/$ Speed $=D / 60$ hours
Total Distance for the Round Trip:
Total Distance $=$ Distance to Chicago + Distance from Chicago $=D+D=2 D$ miles
Total Time for the Round Trip:
Total Time $=$ Time for Trip $1+$ Time for Trip $2=D / 40+D / 60$ hours
To add the fractions, find a common denominator (which is 120):
$D / 40+D / 60=(3 D / 120)+(2 D / 120)=5 D / 120=D / 24$ hours
Average Speed for the Round Trip:
Average Speed = Total Distance / Total Time
Average Speed $=2 D /(D / 24)$
Average Speed $=2 D \times(24 / D)$
Average Speed $=2 \times 24$
Average Speed $=48$ miles per hour
