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19 Nov 2007, 14:37
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Aaron traveled from New York to New Jersey in 45 mins. What was Aoron's average speed?
(1) Aaron traveled 68.9 kilometers on this trip. (1 kilometer = 0.6214 miles)
(2) One-third the distance of the trip was traveled at 50 miles per hour, and the other two thirds of the distance was traveled at 60 miles per hour.
This is an easy question. OA is D. However, i'm not too sure how to set up the equation for statement 2. I know that I can reach to an answer with this information, but i'm just not sure how to create an equation. Would someone please show me how? thank you
(1) Aaron traveled 68.9 kilometers on this trip. (1 kilometer = 0.6214 miles)
(2) One-third the distance of the trip was traveled at 50 miles per hour, and the other two thirds of the distance was traveled at 60 miles per hour.
This is an easy question. OA is D. However, i'm not too sure how to set up the equation for statement 2. I know that I can reach to an answer with this information, but i'm just not sure how to create an equation. Would someone please show me how? thank you
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19 Nov 2007, 14:58
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2)
NY-------0---------------NJ
S- total distance
V1,V2 - speed
Va-average speed
S1,S2 - distance (S1=(NY,0), S2=(0,NJ)
t - time
one knows:
t
S=S1+S2
n=S1/S
m=S2/S
------------------------
t=t1+t2=(S1/V1+S2/V2)
Va=S/t=S/(S1/V1+S2/V2)=(1/(n/V1+m/V2))=V1*V2/(n*V2+m*V1)
Va=50*60/(60/3+50*2/3)=50*60*3/160~56.3 (miles/h)
NY-------0---------------NJ
S- total distance
V1,V2 - speed
Va-average speed
S1,S2 - distance (S1=(NY,0), S2=(0,NJ)
t - time
one knows:
t
S=S1+S2
n=S1/S
m=S2/S
------------------------
t=t1+t2=(S1/V1+S2/V2)
Va=S/t=S/(S1/V1+S2/V2)=(1/(n/V1+m/V2))=V1*V2/(n*V2+m*V1)
Va=50*60/(60/3+50*2/3)=50*60*3/160~56.3 (miles/h)
20 Nov 2007, 01:41
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according to the explanation, this is how they did:
50(1/3) + 60(2/3) = 56 2/3
But honestly, I don't see the logic of this approach. Now imagine you have this problem instead:
Tom drove from his house to school at a spead of 30 mph. Tom then drove through the same road back home at a speed of 40 mph. What was Tom's average speed?
the answer is 34 2/7
now, if i apply the same logic from the first example to the second one, you wouldn't get the right answer cause you would get:
30(1) + 40(1) = 70 which is wrong
so what makes these 2 problems different?
50(1/3) + 60(2/3) = 56 2/3
But honestly, I don't see the logic of this approach. Now imagine you have this problem instead:
Tom drove from his house to school at a spead of 30 mph. Tom then drove through the same road back home at a speed of 40 mph. What was Tom's average speed?
the answer is 34 2/7
now, if i apply the same logic from the first example to the second one, you wouldn't get the right answer cause you would get:
30(1) + 40(1) = 70 which is wrong
so what makes these 2 problems different?
