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March 11th, 2008, 05:21 AM   #1
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Distance, time and rate

To cover the distance of 180 km, with average speed 15 km/h less than expected, took 1 hour longer than expected. Find the average speed.
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March 11th, 2008, 06:28 AM   #2
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If v is the average speed, then the time to cover 180km takes:

t=180/v

Now, you say that if we were going with a speed that's 15 km/h smaller than the average, we would cover the same distance in 1 hour more. So, we have:

180/(v-15) = 180/v+1

180 v/(v-15) = 180+v

180 v = 180(v-15)+v(v-15)

180 v = 180 v-15*180+v(v-15)

0= v^2-15v+15*180

Using the quadratic formula, we get:

v1=-45 v2=60

Since the first answer makes no sense, the answer is v=60.

Checking:

180/(v-15) = 180/v+1

180/(60-15) = 180/60+1

180/(60-15) = 3+1

4=4
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March 11th, 2008, 12:09 PM   #3
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No. The average speed was expected to be 60 km/h, but was actually 45 km/h.
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