You have to assign variables to their speeds and distances. So lets say k is the speed Kim is riding, then you know that the speed Deb is riding is k+3, because deb is riding 3 miles per hour faster.
So after 1.5 hours, together they have ridden 16.5 miles. distance = speed * time , but in this case, you have to take into account both Kim and Deb, because their *total* distance is 16.5 miles, not just one of them.
So
total distance = (kims speed)x(time) + (debs speed)x(time)
16.5 miles = k*1.5 hours + (k+3)*1.5 hours.
16.5 = 1.5k + 1.5k + 4.5
12 = 3k
k = 4
So you know Kims speed is 4 miles per hour.
2007-08-03 02:01:35
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answer #1
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answered by Jon G 4
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Speed is defined as distance / time, written as d/t.
Kim's speed is k. Deb's speed is k+3. Since they were going in opposite directions, the total speed is (k+3) + k or 2k+3.
Since speed = d/t, you can re-write the problem as:
2k+ 3 = 16.5/1.5.
Solving for k gives 4 mph.
2007-08-03 02:03:28
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answer #2
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answered by Scott H 2
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Deb is riding at 7 miles per hour
Kim rides at 4 miles per hour.
In 1.5 hours-:
Deb travels: 7 * 1.5 = 10.5 miles
Kim travels 4 * 1.5 = 6 miles
10.5 + 6 = 16.5 miles (hence proved)
2007-08-03 02:02:34
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answer #3
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answered by Doctor Q 6
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Let k=Kim's speed
d=Deb's speed
d = k+3
Because they ride in opposite direction the distance between them after 1.5 hours is
1.5(d + k) = 16.5
Let's plug d=k+3 into the equation:
1.5(k + 3 + k) = 16.5
1.5(2k + 3) = 16.5 // dividing by 1.5
2k + 3 = 11 // -3
2k = 8 // dividing by 2
k = 4
Kim's speed is 4 MPH.
2007-08-03 02:02:55
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answer #4
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answered by Amit Y 5
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Each girl's distance is calculated by multiplying their speed and their time:
Let Dk = Kim's distance = Vk x Tk
Dd = Deb's distance = Vd x Td
Vk = Kim's velocity (speed)
Vd = Deb's velocity = Vk + 3
Tk = Kim's Time = 1.5 hrs
Td = Deb's Time = 1.5 hrs
So, their combined distances is Dk + Dd = 16.5 miles
Substitute:
(Vk x Tk) + (Vd x Td) = 16.5
(Vk x 1.5) + ((Vk+3) x 1.5) = 16.5
Now you only have 1 variable, Kim's velocity (speed)
1.5·Vk + 1.5·Vk + 4.5 = 16.5
3·Vk + 4.5 = 16.5
3Vk = 12
Vk = 4
Kim was going 4 mph; Deb was going 4+3= 7 mph
Check:
In 1.5 hours, Kim went 1.5 x 4 = 6 miles
In 1.5 hours, Deb went 1.5 x 7 = 10.5 miles
Their combined distance = 16.5 miles
verified.
2007-08-03 02:06:56
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answer #5
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answered by Tony The Dad 3
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We start with an obvious simplification; they will be 11 miles apart in one hour, so are separating at a total of 11 mph. We have (K+3) + K = 11, so 2K = 8 and K = 4.
2007-08-03 02:55:54
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answer #6
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answered by Anonymous
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