English Deutsch Français Italiano Español Português 繁體中文 Bahasa Indonesia Tiếng Việt ภาษาไทย
All categories

Kim and Deb ride bicycles in opposite directions. Deb's speed is three miles per hour faster than Kim. If they are 16.5 miles apart in 1.5 hours, what is the speed of Kim?

Can anyone explain how to do this in detail so I understand how to do it my self in the future.

2007-08-03 01:54:47 · 6 answers · asked by Phych 1 in Science & Mathematics Mathematics

6 answers

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 · answer #1 · answered by Jon G 4 · 0 0

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 · answer #2 · answered by Scott H 2 · 0 0

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 · answer #3 · answered by Doctor Q 6 · 0 0

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 · answer #4 · answered by Amit Y 5 · 0 0

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 · answer #5 · answered by Tony The Dad 3 · 0 0

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 · answer #6 · answered by Anonymous · 0 0

fedest.com, questions and answers