Kayla rode her bike from her house to school at an average speed of 8mph. Then she rode from school back home along the same route at an average speed of 12mph. If the round trip took her 1 hour, how many miles long is the round trip?Explain your answer.
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Anonymous
ANSWERS: 5
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What do we do if Kayla stopped for 15 minutes at school to talk to someone?
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the round trip omits her stop time. 1 hour is the amount of travel time only.
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If you assume zero stop time (normally, I wouldn't put stop time in a round trip time anyway): This is a system of two equations and two unknowns: 8mph * x = 12mph * y x + y = 1 where: x is the time in hours to go to school y is the time in hours to return from school 8x = 12y => 8x - 12y = 0 8x - 12y = 0 x + y = 1 Multiply the bottom equation by 8 and subtract it from the top. Bottom equation is now 8x + 8y = 8. Subtracting it from the top gives: -20y = -8 Solve for y: y = 8/20 = 4/10 = 2/5 hours Substitute that value back in x + y =1 and you get x = 3/5 hours Now you have the time, and you can just use "distance = rate times time" to figure out the distance. 3/5 hours * 8 mph = 24/5 miles. But that's just one half of the round trip, so double that and you get ===> 48/5 miles <===
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Her average speed for the whole trip is 10 miles per hour, so if the round trip took her an hour - it's a ten mile round trip.
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If the distance to school was 24 miles, a number chosen to be divisible by 8 and 12, the times would be 3 hours there and 2 hours back = 5 hours. But it only took 1 hour, which is a fifth as long. So the distance to school is a fifth as long as 24 miles = 4.8 miles and the round trip is 9.6 miles. Check: her average speed is between her two speeds, but nearer to the slower speed than exactly half way between the two. That's what we expect, because she cycled for LONGER at the slower speed than she did the faster one so it counts for more.
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